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Math and science::Topology

Hausdorff spaces

Most interesting topological spaces are Hausdorff. Hausdorffness is identified as being the second separation condition. The first condition, T1 is a sub-requirement of T2 (Housdorff), so it is useful to keep it in mind when thinking about the Hausdorff condition.

T1

A topological space \( X \) is said to be \( T_1 \) iff [...].

Now for Hausdorff.

Hausdorff

A topological space \( X \) is Hausdorff (or \( T_2 \)) iff [...].

Lemma. Every Hausdorff space is \( T_1 \).