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)
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Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
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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
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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