# Existence of Completely Normal Space which is not Perfectly Normal

## Theorem

There exists at least one example of a completely normal topological space which is not perfectly normal.

## Proof

Let $T$ be an uncountable Fort space.

From Fort Space is Completely Normal, $T$ is a completely normal space.

From Uncountable Fort Space is not Perfectly Normal, $T$ is not a perfectly normal space.

Hence the result.

$\blacksquare$