Question

Is a finite codimensional subspace always closed or dense?

score 311 · Answer 1 · 2019-10-31 18:22:57

311

Views

Is a finite codimensional subspace always closed or dense?

Published on 31 Oct 2019 - 18:22

score 117 · Answer 2 · 2023-02-05 20:42:18

117

Views

Understanding dense sets

Published on 05 Feb 2023 - 20:42

score 157 · Answer 3 · 2023-02-05 22:35:27

157

Views

Is it possible to define a topology on the real line such that 0 and non-zero integers are dense but no finite subset of non-zero integers is dense?

Published on 05 Feb 2023 - 22:35

score 46 · Answer 4 · 2026-02-23 04:43:04

46

Views

Characterization of density and adherence in topological space.

Published on 23 Feb 2026 - 4:43

score 56 · Answer 5 · 2023-02-16 00:34:58

56

Views

Extension of non-first countable space

Published on 16 Feb 2023 - 0:34

score 65 · Answer 6 · 2023-02-26 13:44:30

65

Views

How can I show that this set is not dense in $S^1\times S^1$?

Published on 26 Feb 2023 - 13:44

score 134 · Answer 7 · 2023-03-05 19:49:52

134

Views

Rudin's RCA Theorem $4.18$.

Published on 05 Mar 2023 - 19:49

score 53 · Answer 8 · 2023-03-17 18:19:02

53

Views

Hausdorff measure of uncountable dense subsets

Published on 17 Mar 2023 - 18:19

score 46 · Answer 9 · 2023-03-22 12:03:29

46

Views

If $X$ is locally compact, then $\mathrm{Lib}_c (X)$ is dense in $L^p (X, \mu)$ for $p \in [1, \infty)$

Published on 22 Mar 2023 - 12:03

score 164 · Answer 10 · 2023-03-23 15:21:51

164

Views

Proof on why solution to a linear system Ax=b belong to the set of initial abitrary guess plus the Krylov subspace of the matrix & intitial residual?

Published on 23 Mar 2023 - 15:21

score 196 · Answer 11 · 2026-02-23 04:41:37

196

Views

Nowhere dense subsets of a dense subspace are nowhere dense in the whole space and vice versa

Published on 23 Feb 2026 - 4:41

score 67 · Answer 12 · 2026-03-25 11:06:38

67

Views

$\mathcal C_c^\infty (\Omega)$ is dense in $L^\infty (\Omega)$ w.r.t. the weak topology $\sigma(L^\infty, L^1)$

Published on 25 Mar 2026 - 11:06

score 26 · Answer 13 · 2026-03-25 09:25:34

26

Views

Confusion over dense level sets of the Takagi function

Published on 25 Mar 2026 - 9:25

score 85 · Answer 14 · 2026-03-25 11:04:38

85

Views

If $\mu(\Omega) < \infty$, then the space of $\mu$-simple functions is dense in $L^\infty (\Omega)$

Published on 25 Mar 2026 - 11:04

score 101 · Answer 15 · 2023-04-13 13:35:17

101

Views

Linear span of $\{e^{-n x}\}_{n\in\mathbb N}$ is dense in $L^2((0,\infty))$. Explicit expansion?

Published on 13 Apr 2023 - 13:35

List Question

Is a finite codimensional subspace always closed or dense?

Understanding dense sets

Is it possible to define a topology on the real line such that 0 and non-zero integers are dense but no finite subset of non-zero integers is dense?

Characterization of density and adherence in topological space.

Extension of non-first countable space

How can I show that this set is not dense in $S^1\times S^1$?

Rudin's RCA Theorem $4.18$.

Hausdorff measure of uncountable dense subsets

If $X$ is locally compact, then $\mathrm{Lib}_c (X)$ is dense in $L^p (X, \mu)$ for $p \in [1, \infty)$

Proof on why solution to a linear system Ax=b belong to the set of initial abitrary guess plus the Krylov subspace of the matrix & intitial residual?

Nowhere dense subsets of a dense subspace are nowhere dense in the whole space and vice versa

$\mathcal C_c^\infty (\Omega)$ is dense in $L^\infty (\Omega)$ w.r.t. the weak topology $\sigma(L^\infty, L^1)$

Confusion over dense level sets of the Takagi function

If $\mu(\Omega) < \infty$, then the space of $\mu$-simple functions is dense in $L^\infty (\Omega)$

Linear span of $\{e^{-n x}\}_{n\in\mathbb N}$ is dense in $L^2((0,\infty))$. Explicit expansion?

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