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
Now for Hausdorff.
Hausdorff
A topological space
Lemma. Every Hausdorff space is