List questions from locally-convex-spaces

Published on 23 Mar 2026 - 15:03

725

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A linear subspace $Y$ is dense iff there is no trivial funcitonal vanishing on $Y$

Published on 23 Mar 2026 - 15:31

188

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Is a countable product locally convex?

Published on 22 Mar 2026 - 12:10

238

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Reference request: Locally convex space is Hausdorff if and only if ...

Published on 23 Mar 2026 - 13:20

80

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A particular TVS

Published on 23 Mar 2026 - 7:40

59

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Continuity and sequential continuity of a linear functional

Published on 23 Mar 2026 - 1:46

218

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How to show $X := \bigcup_{n \in \mathbb{N}}X_n$ is a locally convex space.

Published on 23 Mar 2026 - 0:05

144

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Joint continuity of bilinear pairing (with unusual topology)

Published on 22 Mar 2026 - 23:03

129

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One assumption in the proof of one result of Hahn-Banach theorem.

Published on 22 Mar 2026 - 20:38

31

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Try to find a seminorm $p$ on a locally convex space st $|f|\leq p$.

Published on 23 Mar 2026 - 11:58

212

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Is a linear functional on a locally convex space $X$ that continuous on a dense subset of X continuous?

Published on 23 Mar 2026 - 0:09

29

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Is this extension continuous on $X$?

Published on 22 Mar 2026 - 8:24

50

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Is the extension in this answer well defined and linear?

Published on 22 Mar 2026 - 18:02

627

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What is the (strong) dual of a projective/inductive limit?

Published on 23 Mar 2026 - 5:57

220

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Is the space of bounded continuous functions on the reals with the topology of uniform convergence on compact sets fully barrelled?

Published on 22 Mar 2026 - 16:25

List Question

Locally convex vector space: Unified polars of zero neighbourhoods are the dual space

A linear subspace $Y$ is dense iff there is no trivial funcitonal vanishing on $Y$

Is a countable product locally convex?

Reference request: Locally convex space is Hausdorff if and only if ...

A particular TVS

Continuity and sequential continuity of a linear functional

How to show $X := \bigcup_{n \in \mathbb{N}}X_n$ is a locally convex space.

Joint continuity of bilinear pairing (with unusual topology)

One assumption in the proof of one result of Hahn-Banach theorem.

Try to find a seminorm $p$ on a locally convex space st $|f|\leq p$.

Is a linear functional on a locally convex space $X$ that continuous on a dense subset of X continuous?

Is this extension continuous on $X$?

Is the extension in this answer well defined and linear?

What is the (strong) dual of a projective/inductive limit?

Is the space of bounded continuous functions on the reals with the topology of uniform convergence on compact sets fully barrelled?

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