Modern Analysis 1
Homework 07
1. Let
X
⊂
R
and let
f
:
X
→
R
map Cauchy sequences to Cauchy sequences.
Prove that if
X
is bounded then
f
is uniformly continuous; also, show by
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Unformatted text preview: example that the boundedness hypothesis may not be dropped. Generalize? 1...
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 Fall '09
 Robinson
 Mathematical analysis, Limit of a sequence, Cauchy sequence, Uniform continuity, Topological vector space, map Cauchy sequences

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