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Corollary: Continuous Functions Mapping Compact Domains to Real Numbers are Bounded
(related to Theorem: Continuous Functions Mapping Compact Domains to Real Numbers Take Maximum and Minimum Values on these Domains)
Let $X$ be a metric spaces, $D\subset X$ be a compact subset and $f:D\mapsto \mathbb R$ a continuous function mapping the domain $D$ to the real numbers $\mathbb R$. Then the function $f$ is bounded.
Table of Contents
Proofs: 1
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Chapters: 1
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References
Bibliography
 Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984