Continuous Image of Compact Space is Compact/Corollary 1

Corollary to Continuous Image of Compact Space is Compact

Compactness is a topological property.

Proof

Follows directly from:

Continuous Image of Compact Space is Compact

the definition of topological property

the definition of homeomorphism.

$\blacksquare$

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $5$: Compact spaces: $5.5$: Continuous maps on compact spaces: Corollary $5.5.2$