Topological indistinguishability is an equivalence relation on any topological space. For a topological space , two (possibly equal, possibly distinct) points are termed topologically indinstinguishable if the following equivalent conditions hold:
- The closures of the singleton sets and are equal.
- Every closed subset containing contains and every closed subset containing contains .
- Every open subset containing contains and every open subset containing contains .
Two distinct points that are not topologically indistinguishable are termed topologically distinguishable.