Compact Space is Pseudocompact

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Theorem

Let $\struct {K, \tau}$ be a compact space.

Then:

$\struct {K, \tau}$ is pseudocompact

Proof

Follows immediately from:

• Compact Space is Countably Compact

• Countably Compact Space is Pseudocompact

$\blacksquare$

Sources

1960: Leonard Gillman and Meyer Jerison: Rings of Continuous Functions: Chapter $1$: Functions on a Topological Space, $\S 1.4$