Editing Separated sets (section)

==Relation to topologically distinguishable points==
{{main|Topological distinguishability}}

Given a topological space ''X'', two points ''x'' and ''y'' are ''topologically distinguishable'' if there exists an [[open set]] that one point belongs to but the other point does not. If ''x'' and ''y'' are topologically distinguishable, then the [[singleton set]]s {''x''} and {''y''} must be disjoint. On the other hand, if the singletons {''x''} and {''y''} are separated, then the points ''x'' and ''y'' must be topologically distinguishable. Thus for singletons, topological distinguishability is a condition in between disjointness and separatedness.