List questions from complete-spaces

Published on 15 Feb 2012 - 7:19

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Which of the following metric spaces are complete?

Published on 11 Jul 2012 - 23:43

341

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Is this metric space complete: $d(f,g)=\max\limits_{t\in[0,1]} |f(t)-g(t)|$ for $C^1$-functions?

Published on 22 Jul 2012 - 12:47

36.7k

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Showing that if a subset of a complete metric space is closed, it is also complete

Published on 26 Nov 2012 - 1:19

18k

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Extension of a Uniformly Continuous Function between Metric Spaces

Published on 26 Nov 2012 - 21:06

824

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Why must a normed space homeomorphic to a complete metric space be complete?

Published on 24 Mar 2013 - 14:05

107

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Completeness and Topology of $\ell ^p,0<p<1$

Published on 01 Aug 2020 - 17:38

53

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Proof of Equivalent Characterisation of Complete Metric Space without using Compactifications

Published on 28 Mar 2026 - 10:16

76

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Completeness of $\mathcal{l}^1$?

Published on 03 Aug 2020 - 12:28

199

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Banach space of continuous and discontinuous functions on R

Published on 05 Aug 2020 - 16:49

159

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Why bother with the space $\mathcal{L}^1$ for integration when we can abstractly deal with the completion of a semi-normed space

Published on 06 Aug 2020 - 2:18

2k

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Is there any metric on R with which it is incomplete.

Published on 28 Mar 2026 - 19:35

48

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Property related to weak lebesgue numbers

Published on 28 Aug 2020 - 19:34

36

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Can closed dense sets in the completion space be no longer closed?

Published on 01 Sep 2020 - 2:48

1.2k

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Formal proof for completion of metric space

Published on 05 Sep 2020 - 13:53

List Question

Totally bounded, complete $\implies$ compact

Which of the following metric spaces are complete?

Is this metric space complete: $d(f,g)=\max\limits_{t\in[0,1]} |f(t)-g(t)|$ for $C^1$-functions?

Showing that if a subset of a complete metric space is closed, it is also complete

Extension of a Uniformly Continuous Function between Metric Spaces

Why must a normed space homeomorphic to a complete metric space be complete?

Completeness and Topology of $\ell ^p,0<p<1$

Proof of Equivalent Characterisation of Complete Metric Space without using Compactifications

Completeness of $\mathcal{l}^1$?

Banach space of continuous and discontinuous functions on R

Why bother with the space $\mathcal{L}^1$ for integration when we can abstractly deal with the completion of a semi-normed space

Is there any metric on R with which it is incomplete.

Property related to weak lebesgue numbers

Can closed dense sets in the completion space be no longer closed?

Formal proof for completion of metric space

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