Question

Let $E$ be an infinite-dimensional t.v.s. Is the map sending $x$ to its $b$-th coordinate continuous?

score 36 · Answer 1 · 2026-03-31 05:36:42

36

Views

Let $E$ be an infinite-dimensional t.v.s. Is the map sending $x$ to its $b$-th coordinate continuous?

Published on 31 Mar 2026 - 5:36

score 37 · Answer 2 · 2022-01-26 13:11:31

37

Views

Excluded point topological spaces

Published on 26 Jan 2022 - 13:11

score 56 · Answer 3 · 2026-03-27 10:08:23

56

Views

The weak topology is compatible with the vector space structure

Published on 27 Mar 2026 - 10:08

score 49 · Answer 4 · 2022-01-27 14:06:31

49

Views

Let $f,h:E \to F$ be continuous functions between topological vector spaces. Then $f+h$ is continuous

Published on 27 Jan 2022 - 14:06

score 68 · Answer 5 · 2026-03-27 10:16:58

68

Views

The weak$^\star$ topology is compatible with the vector space structure

Published on 27 Mar 2026 - 10:16

score 55 · Answer 6 · 2022-01-28 11:51:58

55

Views

On equality of two topologies on the vector space $C(\Omega)$

Published on 28 Jan 2022 - 11:51

score 37 · Answer 7 · 2022-01-30 14:26:52

37

Views

The existence of a sub-open set $V$ of an open set $U$ in $R^n$ such that $V$ contains a compact set $K$.

Published on 30 Jan 2022 - 14:26

score 20 · Answer 8 · 2022-01-30 17:23:47

20

Views

Let $S :=F^E$ be the set of all maps from a set $E$ to a t.v.s. $F$. Then $S$ is also a t.v.s.

Published on 30 Jan 2022 - 17:23

score 96 · Answer 9 · 2022-01-30 22:55:06

96

Views

Topological vector spaces over different topological fields

Published on 30 Jan 2022 - 22:55

score 40 · Answer 10 · 2026-03-31 05:36:17

40

Views

Let $E$ be an infinite-dimensional t.v.s. and $E^\star$ its topological dual. Is it true that $\dim E \le \dim E^\star$?

Published on 31 Mar 2026 - 5:36

score 108 · Answer 11 · 2022-02-02 02:46:16

108

Views

Splitting of a topological vector space (TVS) into an (a) countable sum and (b) direct integral of subspaces

Published on 02 Feb 2022 - 2:46

score 50 · Answer 12 · 2022-02-12 00:22:29

50

Views

Convergent sequence has finitely many nonzero terms

Published on 12 Feb 2022 - 0:22

score 37 · Answer 13 · 2026-03-27 13:19:34

37

Views

$\sigma(M, M')$ coincides with the subspace topology that $\sigma(E, E')$ induces on $M$

Published on 27 Mar 2026 - 13:19

score 35 · Answer 14 · 2022-02-16 13:22:32

35

Views

There is a linear, continuous operator $\widetilde\varphi: H \to F$ that extends $\varphi$ and preserves the norm

Published on 16 Feb 2022 - 13:22

score 28 · Answer 15 · 2026-03-27 00:03:45

28

Views

Is there a common directed set that induces $2$ monotone cofinal maps to $2$ other directed sets?

Published on 27 Mar 2026 - 0:03

List Question

Let $E$ be an infinite-dimensional t.v.s. Is the map sending $x$ to its $b$-th coordinate continuous?

Excluded point topological spaces

The weak topology is compatible with the vector space structure

Let $f,h:E \to F$ be continuous functions between topological vector spaces. Then $f+h$ is continuous

The weak$^\star$ topology is compatible with the vector space structure

On equality of two topologies on the vector space $C(\Omega)$

The existence of a sub-open set $V$ of an open set $U$ in $R^n$ such that $V$ contains a compact set $K$.

Let $S :=F^E$ be the set of all maps from a set $E$ to a t.v.s. $F$. Then $S$ is also a t.v.s.

Topological vector spaces over different topological fields

Let $E$ be an infinite-dimensional t.v.s. and $E^\star$ its topological dual. Is it true that $\dim E \le \dim E^\star$?

Splitting of a topological vector space (TVS) into an (a) countable sum and (b) direct integral of subspaces

Convergent sequence has finitely many nonzero terms

$\sigma(M, M')$ coincides with the subspace topology that $\sigma(E, E')$ induces on $M$

There is a linear, continuous operator $\widetilde\varphi: H \to F$ that extends $\varphi$ and preserves the norm

Is there a common directed set that induces $2$ monotone cofinal maps to $2$ other directed sets?

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