The boundary of a set is a topological notion and may change if one changes the topology. For example, given the usual topology on formula_20, the boundary of a closed disk formula_21 is the disk's surrounding circle: formula_22. If the disk is viewed as a set in formula_23 with its own usual topology, i.e. formula_24, then the boundary of the disk is the disk itself: formula_25. If the disk is viewed as its own topological space (with the subspace topology of formula_20), then the boundary of the disk is empty.