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Does every vector space with a weak topology contain a dense subspace which is a direct sum of real lines?

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#topological-vector-spaces #direct-sum #weak-topology
87
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Every complete topological vector space is metrizable

Published on
#general-topology #analysis #topological-vector-spaces
158
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Dual space of t.v.s. endowed with weak topology

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#general-topology #vector-spaces #topological-vector-spaces
263
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Compactness of open map

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#general-topology #functional-analysis #convergence-divergence #banach-spaces #topological-vector-spaces
236
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Where is Axiom of Choice used in the proof of Riesz and/or Hahn-Banach extension theorems?

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#reference-request #functional-analysis #banach-spaces #topological-vector-spaces #hahn-banach-theorem
50
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Fixed Point Theorem in Topological vector spaces

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#functional-analysis #partial-differential-equations #sobolev-spaces #fixed-point-theorems #topological-vector-spaces
80
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Linear Subspace of a topological space

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#vector-spaces #continuity #topological-vector-spaces
598
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Why is $X^*$ with the weak-* topology not a locally compact vector space?

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#general-topology #functional-analysis #compactness #topological-vector-spaces #fake-proofs
526
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How to prove the Heine-Borel property for Fréchet spaces?

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#real-analysis #functional-analysis #partial-differential-equations #harmonic-analysis #topological-vector-spaces
368
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Proof that the Schwartz space is Montel, i.e., is of the Heine-Borel property.

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#functional-analysis #partial-differential-equations #fourier-transform #harmonic-analysis #topological-vector-spaces
259
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Why is a vector space with weak topology a topological vector space?

Published on
#topological-vector-spaces
163
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Definition of Complemented Subspaces in a Topological Vector Space

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#general-topology #functional-analysis #definition #normed-spaces #topological-vector-spaces
136
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If $B$ is a metrizable, complete subset of a topological vector space, must $B$ be closed?

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#general-topology #topological-vector-spaces
96
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Does the dual of this cone have a non-empty interior?

Published on
#functional-analysis #topological-vector-spaces #duality-theorems
450
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A characterization for closed sets in topological vector spaces

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#weak-convergence #topological-vector-spaces #nets

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