# Paracompact Countably Compact Space is Compact

## Theorem

Let $T = \struct {S, \tau}$ be a countably compact space which is also paracompact.

Then $T$ is compact.

## Proof

From the definition of paracompact space, a paracompact space is also a metacompact space.

The result follows from Metacompact Countably Compact Space is Compact.

$\blacksquare$