Separation axioms

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In topology, separation axioms describe classes of topological spaces according to how well the open sets of the topology distinguish between distinct points.

[edit] Terminology

A neighbourhood of a point x in a topological space X is a set N such that x is in the interior of N; that is, there is an open set U such that x \in U \subseteq N. A neighbourhood of a set A in X is a set N such that A is contained in the interior of N; that is, there is an open set U such that A \subseteq U \subseteq N.

Subsets U and V are separated in X if U is disjoint from the closure of V and V is disjoint from the closure of U.

A Urysohn function for subsets A and B of X is a continuous function f from X to the real unit interval such that f is 0 on A and 1 on B.

[edit] Axioms

A topological space X is

[edit] Properties

[edit] References

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