Separated Sets - Relation To Topologically Distinguishable Points

Relation To Topologically Distinguishable Points

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 sets {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.

For more about topologically distinguishable points, see Topological distinguishability.

Read more about this topic:  Separated Sets

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