\(
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\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
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\require{physics}
\require{ams}
\require{mathtools}
\)
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 \( T_1 \).
