Continuous Image of Compact Space is Compact/Corollary 1
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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 $5.5.2$