Question

Showing that the metric $d(n, m) = 2^{-r}$ if $|n - m| = 2^{r}t$ with $t$ odd if $n \neq m$ and $d_2(n, n) = 0$ on $\mathbb Z$ is not complete

score 39 · Answer 1 · 2022-10-12 20:41:42

39

Views

Showing that the metric $d(n, m) = 2^{-r}$ if $|n - m| = 2^{r}t$ with $t$ odd if $n \neq m$ and $d_2(n, n) = 0$ on $\mathbb Z$ is not complete

Published on 12 Oct 2022 - 20:41

score 155 · Answer 2 · 2022-10-13 13:11:37

155

Views

Use of theorem 3.5 Rudin's Functional Analysis to show simple functions are dense in $L^p$

Published on 13 Oct 2022 - 13:11

score 102 · Answer 3 · 2026-03-25 14:34:37

102

Views

Is it true, that, metrizable field is locally compact iff complete (in topology Induced by Metric)?

Published on 25 Mar 2026 - 14:34

score 68 · Answer 4 · 2022-10-13 16:19:46

68

Views

Prove that $\mathbb{Q}$ with the topology induced by the usual distance is not complete.

Published on 13 Oct 2022 - 16:19

score 449 · Answer 5 · 2022-10-16 17:30:49

449

Views

If $d_1$ and $d_2$ are two equivalent metric on $X$ then is $X$ complete with respect $d_1$ if and only if it is complete with respect $d_2$?

Published on 16 Oct 2022 - 17:30

score 299 · Answer 6 · 2022-10-17 10:08:04

299

Views

Another completion of $\overline{\Bbb{Q}}$

Published on 17 Oct 2022 - 10:08

score 89 · Answer 7 · 2022-10-18 17:55:19

89

Views

Prove that any normed vector space with finite dimension is complete.

Published on 18 Oct 2022 - 17:55

score 142 · Answer 8 · 2026-03-29 09:18:58

142

Views

Normalization of Vector in arbitrary Normed Vector Space

Published on 29 Mar 2026 - 9:18

score 136 · Answer 9 · 2026-03-29 20:01:25

136

Views

How the weak$^*$ topology of the space of all Borel probability measures on $X$ is defined?

Published on 29 Mar 2026 - 20:01

score 65 · Answer 10 · 2026-02-24 00:46:46

65

Views

Why is $K^{\mathrm{sep}}$ dense in $K_v^{\mathrm{sep}}$?

Published on 24 Feb 2026 - 0:46

score 97 · Answer 11 · 2022-10-24 18:34:59

97

Views

Completeness of French railroad metric space

Published on 24 Oct 2022 - 18:34

score 36 · Answer 12 · 2022-10-26 12:05:42

36

Views

Completeness of normed linear space $C^1[0,1]$

Published on 26 Oct 2022 - 12:05

score 137 · Answer 13 · 2022-10-29 14:23:11

137

Views

Question regarding one approach to showing that the vector space $C[0, 1]$ is not complete w.r.t. the $L1$ integral norm

Published on 29 Oct 2022 - 14:23

score 44 · Answer 14 · 2022-11-01 06:06:52

44

Views

Find the Completion of (X, d) where $X = \{\{x_n\} : \sum_{n=1}^\infty 2^n \vert{x_n}\vert < \infty\}$ and $d(x,y) = sup_n \vert x_n - y_n \vert$

Published on 01 Nov 2022 - 6:06

score 135 · Answer 15 · 2022-11-01 06:39:43

135

Views

Does every incomplete real inner product space admit a closed subspace of countable dimension?

Published on 01 Nov 2022 - 6:39

List Question

Showing that the metric $d(n, m) = 2^{-r}$ if $|n - m| = 2^{r}t$ with $t$ odd if $n \neq m$ and $d_2(n, n) = 0$ on $\mathbb Z$ is not complete

Use of theorem 3.5 Rudin's Functional Analysis to show simple functions are dense in $L^p$

Is it true, that, metrizable field is locally compact iff complete (in topology Induced by Metric)?

Prove that $\mathbb{Q}$ with the topology induced by the usual distance is not complete.

If $d_1$ and $d_2$ are two equivalent metric on $X$ then is $X$ complete with respect $d_1$ if and only if it is complete with respect $d_2$?

Another completion of $\overline{\Bbb{Q}}$

Prove that any normed vector space with finite dimension is complete.

Normalization of Vector in arbitrary Normed Vector Space

How the weak$^*$ topology of the space of all Borel probability measures on $X$ is defined?

Why is $K^{\mathrm{sep}}$ dense in $K_v^{\mathrm{sep}}$?

Completeness of French railroad metric space

Completeness of normed linear space $C^1[0,1]$

Question regarding one approach to showing that the vector space $C[0, 1]$ is not complete w.r.t. the $L1$ integral norm

Find the Completion of (X, d) where $X = \{\{x_n\} : \sum_{n=1}^\infty 2^n \vert{x_n}\vert < \infty\}$ and $d(x,y) = sup_n \vert x_n - y_n \vert$

Does every incomplete real inner product space admit a closed subspace of countable dimension?

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