What properties determine dimension in lattice theory? [SEP] It is conserved by perspective mappings ("perspectivities") and ordered by inclusion.
entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment entailment entailment not_entailment not_entailment entailment entailment not_entailment entailment entailment not_entailment not_entailment not_entailment entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment not_entailment entailment entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment not_entailment entailment not_entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment not_entailment entailment not_entailment entailment entailment entailment not_entailment not_entailment not_entailment not_entailment entailment not_entailment entailment entailment