Show that if I := [a, b] and f : I R is increasing on I,

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Show that if I := [a, b] and f : I → R is increasing on I, then f is continuous at a if and only if f (a) = inf{ f(x) : x ∈ (a, b]}.
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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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