1. Let A CX be a metric subspace of a metric space X. Show that A is totally bounded if and only if for any e > 0, there is a finite set {x₁,...,n} CX such that n ACU Be(x₂) i=1
1. Let A CX be a metric subspace of a metric space X. Show that A is totally bounded if and only if for any e > 0, there is a finite set {x₁,...,n} CX such that n ACU Be(x₂) i=1
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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![1. Let A C X be a metric subspace of a metric space X. Show that A is totally bounded
if and only if for any ɛ > 0, there is a finite set {x₁,...,xn} CX such that
n
AC U Be (x₂)
i=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe72e13b-12e8-4646-917c-376e7356872c%2F3cad67f6-9c52-47a3-be0e-205ecca4adee%2Fqkpzjgo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let A C X be a metric subspace of a metric space X. Show that A is totally bounded
if and only if for any ɛ > 0, there is a finite set {x₁,...,xn} CX such that
n
AC U Be (x₂)
i=1
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