Branches History Index

◀ ▲ ▶Branches / Analysis / Proposition: Image of a Compact Set Under a Continuous Function

Proposition: Image of a Compact Set Under a Continuous Function

Let \(X,Y\) be metric spaces and let $f:X\mapsto Y$ a continuous function. If \(C\subset X\) is compact, then the image of $C$ under $f$, i.e. the subset \(f( C)\subset Y\), is also compact.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs

References

Bibliography

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