Infinite Particular Point Space is not Countably Paracompact

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Theorem

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


Then $T$ is not countably paracompact.


Proof

Aiming for a contradiction, suppose $T$ is countably paracompact.

From Countably Paracompact 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.

$\blacksquare$