List questions from locally-convex-spaces

Published on 25 Mar 2026 - 7:45

726

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

Published on 25 Mar 2026 - 7:48

191

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Is a countable product locally convex?

Published on 09 Apr 2026 - 20:26

239

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

Published on 25 Mar 2026 - 7:43

82

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A particular TVS

Published on 05 Apr 2026 - 13:34

60

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Continuity and sequential continuity of a linear functional

Published on 25 Mar 2026 - 9:22

219

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

Published on 25 Mar 2026 - 7:45

145

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Joint continuity of bilinear pairing (with unusual topology)

Published on 25 Mar 2026 - 9:27

130

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

Published on 25 Mar 2026 - 7:46

32

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

Published on 25 Mar 2026 - 7:44

213

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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 25 Mar 2026 - 9:31

31

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Is this extension continuous on $X$?

Published on 06 Apr 2026 - 5:44

51

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Is the extension in this answer well defined and linear?

Published on 25 Mar 2026 - 7:41

628

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

Published on 25 Mar 2026 - 11:13

221

Views

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

Published on 25 Mar 2026 - 7:45

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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