Let A R and let f : A R be continuous at a point c

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Let A ⊂ R and let f : A → R be continuous at a point c ∈ A. Show that for any ε > 0, there exists a neighborhood Vδ(c) of c such that if x; y ∈ A ∩ Vδ(c), then |f(x) - f(y)| < ε.
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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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