Existence of Metacompact Space which is not Paracompact

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Theorem

There exists at least one example of a metacompact topological space which is not also a paracompact space.


Proof

Let $T$ be the Dieudonné plank.


From Dieudonné Plank is Metacompact, $T$ is a metacompact space.

From Dieudonné Plank is not Paracompact, $T$ is not a paracompact space.

Hence the result.

$\blacksquare$


Sources