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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

  1. Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984