Relation To Separation Axioms and Separated Spaces
The separation axioms are various conditions that are sometimes imposed upon topological spaces which can be described in terms of the various types of separated sets. As an example, we will define the T2 axiom, which is the condition imposed on separated spaces. Specifically, a topological space is separated if, given any two distinct points x and y, the singleton sets {x} and {y} are separated by neighbourhoods.
Separated spaces are also called Hausdorff spaces or T2 spaces. Further discussion of separated spaces may be found in the article Hausdorff space. General discussion of the various separation axioms is in the article Separation axiom.
Read more about this topic: Separated Sets
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