Hausdorff Topological Space

Statements

Definition. A topological space $(X,\tau )$ is Hausdorff if for every two distinct points $x,y\in X$, there exist disjoint open sets $U,V\subseteq X$ such that $x\in U$ and $y\in V$. A Hausdorff space is normal if given any two disjoint closed sets $F,G$ in $X$, there exist disjoint open sets $U,V$ such that $F\subset U$ and $G\subset V$.

References

@Tu11, Definition A.16