# Infinite Particular Point Space is not Metacompact

## Theorem

Let $T = \left({S, \tau_p}\right)$ be an infinite particular point space.

Then $T$ is not metacompact.

## Proof

Aiming for a contradiction, suppose $T$ is metacompact.

From Metacompact Space is Countably Metacompact it follows that $T$ is countably metacompact.

But we have that Infinite Particular Point Space is not Countably Metacompact.

Hence the result by Proof by Contradiction.

$\blacksquare$