List questions from metric-spaces

Published on 01 Apr 2026 - 9:32

141

Views

Possible metrics on the space $C[0,1]$?

Published on 09 Apr 2026 - 11:52

52

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Determining open subsets

Published on 08 Aug 2019 - 12:58

120

Views

Induced metric on product of normed spaces?

Published on 09 Apr 2026 - 7:32

13

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If $x_0,h$ belong to a metric vector space and $ε>0$, is there always a sequence $(t_n)_{n∈\mathbb N}\subseteq\mathbb R$ with $x_0+t_nh\in B_ε(x_0)$?

Published on 01 Mar 2026 - 10:18

31

Views

Problem II.3.7: $c_0$ is a closed subspace of $\ell_\infty$

Published on 03 Apr 2026 - 17:53

133

Views

Open set is an increasing union of regular open sets?

Published on 25 Mar 2026 - 10:54

674

Views

Kuratowski convergence and Hausdorff metric

Published on 25 Mar 2026 - 7:43

67

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Compactness in the metric space of all bounded and unbounded complex sequences

Published on 09 Aug 2019 - 15:06

84

Views

Is this an equivalent definition of cluster point?

Published on 09 Aug 2019 - 16:29

317

Views

Is the space $C^1[a,b]$ with its usual 'sup-norm ' topology is separable?

Published on 10 Aug 2019 - 6:10

35

Views

How to understand the notation $(\Sigma \oplus l_{p_k})_2$?

Published on 10 Aug 2019 - 9:51

57

Views

Completeness of subsets in $\mathbb{R}$

Published on 10 Aug 2019 - 15:50

437

Views

Open set that is the intersection of sets in a metric space

Published on 10 Aug 2019 - 16:27

109

Views

In $\mathbb{R}$ with an arbitrary metric, is it true that $d(x, 0) \leq d(x,y)$ for all $x > 0$, $y < 0$?

Published on 10 Aug 2019 - 20:39

List Question

Giving a sequential proof of the Heine-Borel theorem

Possible metrics on the space $C[0,1]$?

Determining open subsets

Induced metric on product of normed spaces?

If $x_0,h$ belong to a metric vector space and $ε>0$, is there always a sequence $(t_n)_{n∈\mathbb N}\subseteq\mathbb R$ with $x_0+t_nh\in B_ε(x_0)$?

Problem II.3.7: $c_0$ is a closed subspace of $\ell_\infty$

Open set is an increasing union of regular open sets?

Kuratowski convergence and Hausdorff metric

Compactness in the metric space of all bounded and unbounded complex sequences

Is this an equivalent definition of cluster point?

Is the space $C^1[a,b]$ with its usual 'sup-norm ' topology is separable?

How to understand the notation $(\Sigma \oplus l_{p_k})_2$?

Completeness of subsets in $\mathbb{R}$

Open set that is the intersection of sets in a metric space

In $\mathbb{R}$ with an arbitrary metric, is it true that $d(x, 0) \leq d(x,y)$ for all $x > 0$, $y < 0$?

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