a) Let E be a nonempty subset of X. Prove that a is a cluster point of

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a) Let E be a nonempty subset of X. Prove that a is a cluster point of E if and only if for each r > 0, E ∩ Br(a) \ (a) is nonempty.
b) Prove that every bounded infinite subset of R has at least one cluster point.

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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 04:16 AM

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a) Let E be a nonempty subset of X. Prove that a is a cluster point of

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a Surely a set which has infinitely many points is nonempty Conversely if E B s a n a i...View the full answer

An Introduction to Analysis

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