Is a one point space Hausdorff?

Question

This may be a silly question but I'll ask anyway: Is a topological space consisting of a single point Hausdorff?

Answer 1

Yes. If $X$ is a one-point topological space, then for any distinct points $x_1\neq x_2$ in $X$ there are disjoint open sets $U_1\ni x_1$ and $U_2\ni x_2$.

(Of course, this is vacuously true: for any distinct points $x_1\neq x_2$ in $X$, there is also a pink elephant named Steve.)