List questions from complete-spaces

Published on 15 Sep 2016 - 20:31

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Why do uniformly continuous functions form a Banach space (with the sup norm)?

Published on 17 Sep 2016 - 12:56

371

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Show that $V[a,b]$ is a Banach space

Published on 26 Mar 2026 - 17:31

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Prove $\mathbb R^n$ is complete with respect to non-standard norms

Published on 20 Sep 2016 - 15:39

49

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Is $\mathbb{R}$ complete under the $\frac{t}{2^k(1+t)}$ metric?

Published on 21 Sep 2016 - 23:20

1k

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If $X$ is a dense subspace of a complete metric space $Y$, is $Y$ necessarily the completion of $X$?

Published on 24 Sep 2016 - 9:10

67

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Continuous functions in a complete metric space

Published on 26 Sep 2016 - 8:00

250

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Complete ordered space

Published on 23 Feb 2026 - 8:34

378

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Show that metric space is complete.

Published on 03 Oct 2016 - 20:21

88

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Completeness of the union

Published on 10 Oct 2016 - 15:07

102

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Vector space $V$ complete implies subset of $V$ complete

Published on 13 Oct 2016 - 5:39

51

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How to prove the completeness of $l^\infty_\mathbb{F}$?

Published on 19 Oct 2016 - 20:56

273

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How is it that $d(x,y)=|{\rm arctan}\ x -{\rm arctan}\ y| $ isn't a complete metric space?

Published on 26 Oct 2016 - 5:06

169

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Show that the space $X$ of Lipschitz functions $f$ on $[-1,1]$ with $f(0)=0$ is a banach space

Published on 27 Oct 2016 - 12:37

598

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Subset of continuous functions that are not surjective is open (with sup metric)

Published on 27 Oct 2016 - 13:24

List Question

Complete? subspace of $R^n$ with $||.||_\infty$

Why do uniformly continuous functions form a Banach space (with the sup norm)?

Show that $V[a,b]$ is a Banach space

Prove $\mathbb R^n$ is complete with respect to non-standard norms

Is $\mathbb{R}$ complete under the $\frac{t}{2^k(1+t)}$ metric?

If $X$ is a dense subspace of a complete metric space $Y$, is $Y$ necessarily the completion of $X$?

Continuous functions in a complete metric space

Complete ordered space

Show that metric space is complete.

Completeness of the union

Vector space $V$ complete implies subset of $V$ complete

How to prove the completeness of $l^\infty_\mathbb{F}$?

How is it that $d(x,y)=|{\rm arctan}\ x -{\rm arctan}\ y| $ isn't a complete metric space?

Show that the space $X$ of Lipschitz functions $f$ on $[-1,1]$ with $f(0)=0$ is a banach space

Subset of continuous functions that are not surjective is open (with sup metric)

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