Hausdorff space

definition

Definition

For a topological space $(X,\tau )$ it is called Hausdorff if for distinct points $x\ne y$ then there exits disjoint open sets $U,V\in \tau$ such that $x\in U$ and $y\in V$

Intuition/ usefullness

Hausdorff spaces are nice to work with since they can help to distinguish limits.