Existence of Metacompact Space which is not Paracompact

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.