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 $$T_1$$.