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Definition: Open Function, Closed Function

Let \(X\) und \(Y\) be topological spaces. A continuous function \(f:X\longrightarrow Y\,\) is called:

• open, if the images \(f(A)\) of open subsets \(A\subseteq X\) are open subsets \(f(A)\subseteq Y\).
• closed, if the images \(f(A)\) of closed subsets \(A\subseteq X\) are closed subsets \(f(A)\subseteq Y\).

Mentioned in:

Proofs: 1
Propositions: 2

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References

Adapted from CC BY-SA 3.0 Sources:

1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück