List questions from topological-vector-spaces

Published on 03 Jun 2020 - 0:21

130

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Find continuous functions on $[0,1]$ satisfying this inequality.

Published on 03 Jun 2020 - 17:17

54

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A filter in a subset of a topological vector space by a sequence

Published on 03 Jun 2020 - 22:41

74

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Why do we care about the Bishop-de-Leeuw theorem?

Published on 06 Jun 2020 - 13:45

48

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If $E$ and $F$ are two topological vector spaces Hausdorff, $\hat{E} \times \hat{F} \cong (E\times F)\hat{}$.

Published on 26 Mar 2026 - 21:10

2.9k

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Definition of weak-$*$ topology

Published on 07 Jun 2020 - 13:32

78

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$E$ is a compact Hausdorff TVS $\Leftrightarrow $ $E=\{0\}$.

Published on 08 Jun 2020 - 20:26

92

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Prove that the balanced hull of a compact subset $K$ of a Hausdorff TVS $E$ is compact

Published on 09 Jun 2020 - 13:06

108

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extension of linear maps between Banach spaces

Published on 09 Jun 2020 - 13:41

32

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The natural injection of $E$ into $\hat{E}$ is linear.

Published on 09 Jun 2020 - 14:29

187

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Prove that $\hat{\mathscr{F}} \rightarrow \hat{x}$, where $\hat{x}=\{\mathscr{F} \in \mathscr{C}_E: \mathscr{F} \sim_R i^{-1}(\mathscr{F}')\}$.

Published on 26 Mar 2026 - 17:33

98

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New norm with strictly coarser induced topolgy

Published on 10 Jun 2020 - 15:53

55

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Define a filter base according to a net

Published on 25 Mar 2026 - 19:10

66

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Show that $K$ of a topological space $(X, \tau)$ is compact.

Published on 13 Jun 2020 - 0:28

48

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If $\phi\in W^U$ and if $\psi\in W^V$ and if $W$ is a topological vector space then $f(u,v):=\phi(u)+_{_{W}}(-1)*_{_{W}}\psi(v)$ is continuous

Published on 14 Jun 2020 - 17:25

List Question

Properties of the neighborhoods of $0$ in the cofinite topology

Find continuous functions on $[0,1]$ satisfying this inequality.

A filter in a subset of a topological vector space by a sequence

Why do we care about the Bishop-de-Leeuw theorem?

If $E$ and $F$ are two topological vector spaces Hausdorff, $\hat{E} \times \hat{F} \cong (E\times F)\hat{}$.

Definition of weak-$*$ topology

$E$ is a compact Hausdorff TVS $\Leftrightarrow $ $E=\{0\}$.

Prove that the balanced hull of a compact subset $K$ of a Hausdorff TVS $E$ is compact

extension of linear maps between Banach spaces

The natural injection of $E$ into $\hat{E}$ is linear.

Prove that $\hat{\mathscr{F}} \rightarrow \hat{x}$, where $\hat{x}=\{\mathscr{F} \in \mathscr{C}_E: \mathscr{F} \sim_R i^{-1}(\mathscr{F}')\}$.

New norm with strictly coarser induced topolgy

Define a filter base according to a net

Show that $K$ of a topological space $(X, \tau)$ is compact.

If $\phi\in W^U$ and if $\psi\in W^V$ and if $W$ is a topological vector space then $f(u,v):=\phi(u)+_{_{W}}(-1)*_{_{W}}\psi(v)$ is continuous

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