a) Prove that every convex set in Rn is connected. b) Show that the converse of part

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a) Prove that every convex set in Rn is connected.
b) Show that the converse of part a) is false.
c) Suppose that f: R → R. Prove that f is convex (as a function) if and only if E: = {(x, y): y > f(x)} is convex (as a set in R2).

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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 04:21 AM

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a) Prove that every convex set in Rn is connected. b) Show that the converse of part

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a Suppose E is convex but not connected Then there is a pair of open sets U V which separates E Let ...View the full answer

An Introduction to Analysis

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