Suppose that X and Y are metric spaces and that f : X Y. If X

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Suppose that X and Y are metric spaces and that f : X → Y. If X is compact and connected, and if to every x ∈ X there corresponds an open ball Bx such that x ∈ Bx and f(y) = f(x) for all y ∈ Bx, prove that f is constant on X.

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 04:17 AM

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Suppose that X and Y are metric spaces and that f : X Y. If X

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For each x X f is constant on Bx Since X is compact an...View the full answer

An Introduction to Analysis

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