metric structures.

Ideally, it would be necessary to have such a formal theory of space-time that would be able acquire a most sudden appearance relevant to a concrete model. This approach may be exemplified by obtaining in [@GT] from the same set of axioms, only at the expense of model (topos) choice, either the flat Minkowski space-time, or the curved space-time of general relativity. “Topos theory (see ref. [@Go; @Jo]) offers an independent (of the set theory) approach to the foundations of mathematics. Topoi are categories with “set-like”, objects, “function-like” arrows and “Boolean-like” logic algebras. Handling “sets”, and “functions”, in a topos may differ from that in classical mathematics (i.e. the topos [**Set**]{} of sets): there are non-classical versions of mathematics, each with its non-Boolean version of logic. One possible view on topoi is this: abstract worlds, universes for mathematical discourse, “inhabitants” (researchers) of which may use non-Boolean logics in their reasoning. From this viewpoint the main business of classical physics is to construct models of the objective (absolute) universe with a given “bivalent Boolean” model of the researcher, and choose the most adequate one” [@Tr].

The topos-theoretical approach to theory of space-time has many preferences since for one formal 