Existence of T4 Space which is not T3 1/2

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Theorem

There exists at least one example of a topological space which is a $T_4$ space, but is not also a $T_{3 \frac 1 2}$ space.


Proof

Let $T$ be a Hjalmar Ekdal space.


From Hjalmar Ekdal Space is $T_4$, $T$ is a $T_4$ space.

From Hjalmar Ekdal Space is not $T_{3 \frac 1 2}$ Space, $T$ is not a $T_{3 \frac 1 2}$ space.

Hence the result.

$\blacksquare$


Sources