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Proposition: Continuity of Compositions of Functions

Let $(X,\mathcal O_X),$ $(Y,\mathcal O_Y),$ and $(Z,\mathcal O_Z)$ be topological spaces. Let $f:X\to Y$ and $g:Y\to Z$ be continuous functions. Then the composition $g\circ f:X\to Z$ is continuous.

Table of Contents

Proofs: 1

Mentioned in:

Definitions: 1 2 3
Proofs: 4 5
Propositions: 6

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References

Bibliography

1. Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
2. Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition