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15
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Is the Fréchet quotient space given by the induced seminorms?

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#quotient-spaces #topological-vector-spaces #frechet-space
16
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On a class of compacts broader then Eberlein's

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#general-topology #functional-analysis #topological-vector-spaces #locally-convex-spaces
42
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Equivalent definitions of bounded sets in topological vector spaces

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#general-topology #functional-analysis #analysis #topological-vector-spaces #locally-convex-spaces
30
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Scales of a bounded neighborhood of $0$ forms a neighborhood basis of $0$.

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#general-topology #functional-analysis #analysis #topological-vector-spaces
55
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If $\overline A$ is compact, then $\overline A=\overline A^w$

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#general-topology #functional-analysis #analysis #solution-verification #topological-vector-spaces
177
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Why is $C^\infty(\Omega)$ complete?

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#functional-analysis #analysis #solution-verification #proof-explanation #topological-vector-spaces
207
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Why does $C^\infty(\Omega)$ have the Heine-Borel property?

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#functional-analysis #analysis #solution-verification #proof-explanation #topological-vector-spaces
67
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Closure of balanced convex set and its dilation

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#functional-analysis #normed-spaces #banach-spaces #topological-vector-spaces
26
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For non second-countable TVS, is the sum of measurable functions again measurable?

Published on
#measure-theory #topological-vector-spaces #measurable-functions #borel-sets #second-countable
89
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What is the relationship between convex conjugate and polar set?

Published on
#functional-analysis #convex-analysis #topological-vector-spaces #dual-spaces
19
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The coordinate map of a one-dimensional TVS is continuous

Published on
#solution-verification #continuity #topological-vector-spaces
59
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Textbook on TVS that contains Theorem 32.2 about the completeness of the space of continuous linear maps

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#functional-analysis #reference-request #topological-vector-spaces #locally-convex-spaces
21
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If $x_d \to 0_E$ and $\sup_{d\in D} |\lambda_d| <\infty$, then $\lambda_d x_d \to 0_E$

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#convergence-divergence #solution-verification #topological-vector-spaces #nets
59
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Let $E$ be a TVS and $f:E \to \mathbb R^n$ linear. If $\ker f$ is closed, then $f$ is continuous at $0_E$

Published on
#functional-analysis #continuity #topological-vector-spaces
34
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Having trouble on understanding some parts of Pedersen's explanation of constructing a locally convex topological vector space.

Published on
#linear-algebra #functional-analysis #analysis #topological-vector-spaces

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