Continuous Image of Compact Space is Compact/Corollary 2
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Corollary to Continuous Image of Compact Space is Compact
A continuous mapping from a compact topological space to a metric space is bounded.
Proof
Follows from Continuous Image of Compact Space is Compact and Compact Subspace of Metric Space is Bounded.
$\blacksquare$
Sources
- 1953: Walter Rudin: Principles of Mathematical Analysis ... (previous) ... (next): $4.15$
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $5$: Compact spaces: $5.5$: Continuous maps on compact spaces: Corollary $5.5.3$