T28 needs an argument

[Moniker1998]

Theorem is $T_2$ + countably compact + first countable $\implies T_3$.

As of right now it redirects to Counterexamples.

The proof is like this:

Pick a point $x$ and a closed set $A$ with $x\notin A$. Let $U_n$ be a countable neighbourhood basis for $x$. The sets $A\setminus \overline{U_n}$ are an open cover of $A$ from Hausdorff, and so there exists a finite subcover. Extract from this a neighbourhood $U$ of $x$ with $x\in U$ and $\overline{U}\cap A = \emptyset$.

[prabau]

Yes, we should give an explicit proof, or refer to some existing MSE post if there is a good one (I imagine there must be one already).