Proof That Composition of Continuous Functions Gives a Continuous Function

University Maths Notes

Proof That Composition of Continuous Functions Gives a Continuous Function

Proof That Composition of Continuous Functions Gives a Continuous Function

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Theorem

Letandbe continuous functions.

The composite functionis continuous.

Proof

Letrepresent an open subset ofSinceis continuous,is an open subset of

Sinceis continuous andis an open subset ofis an open subset of

Henceis an open subset ofandis continuous.

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