Existence of Completely Normal Space which is not Perfectly Normal

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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.

$\blacksquare$


Sources