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Proposition: Compositions of Continuous Functions on a Whole Domain

Let \(f:D\to\mathbb R\) and \(g:E\to\mathbb R\) be real functions with \(f(D)\subseteq E\) such that \(f\) is continuous on \(D\) and \(g\) is continuous on \(f(D)\). Then their composition. \[g\circ f:D\to\mathbb R\] is continuous on \(D\).

Table of Contents

Proofs: 1

Mentioned in:

Corollaries: 1
Proofs: 2
Propositions: 3

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983