Points are closed in $T_1$ and Hausdorff spaces

Let \(X\) be a topological space in which every one-point set is closed, that is, a \(T_1\) space. Then every finite subset of \(X\) is closed. Every Hausdorff space is \(T_1\), so in a Hausdorff space every finite subset, in particular every singleton, is closed [@Mun00].