Infinite Particular Point Space is not Countably Paracompact
Jump to navigation
Jump to search
Theorem
Let $T = \struct {S, \tau_p}$ 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.
$\blacksquare$