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What's the definition of proper subspace of a vector space used in Rudin's Functional analysis

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#functional-analysis #vector-spaces #definition #topological-vector-spaces
736
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$C^{\infty}(\mathbb{R})$ as a Fréchet space

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#real-analysis #general-topology #functional-analysis #topological-vector-spaces
75
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Generated space by the harmonic oscillators $e^{iw}$.

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#convergence-divergence #exponential-function #fourier-series #lp-spaces #topological-vector-spaces
101
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Predual of Morrey space

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#functional-analysis #partial-differential-equations #harmonic-analysis #topological-vector-spaces
239
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Function spaces from a geometrical viewpoint.

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#geometry #functional-analysis #reference-request #topological-vector-spaces
75
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Rudin functional analysis, section 3.8 (Topological preliminaries)

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#functional-analysis #topological-vector-spaces #weak-topology
183
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Lemma 3.9 Rudin's functional analysis

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#functional-analysis #topological-vector-spaces
312
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Prove the mapping $(x,y)\mapsto x+y$ from $X \times X \to X$ is continuous when $X$ is given a weak topology.

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#general-topology #functional-analysis #topological-vector-spaces #product-space #weak-topology
153
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Balanced set in $\mathbb{K}$

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#general-topology #topological-vector-spaces
63
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Locally Convex tvs closure of $\{0\}$

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#functional-analysis #topological-vector-spaces #locally-convex-spaces
95
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$\ell^2$ as colimit in $\mathbf{TopVect}_{\mathbb{R}}$

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#vector-spaces #category-theory #lp-spaces #topological-vector-spaces #limits-colimits
171
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Is every normable topological vector space "inner productable"?

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#general-topology #examples-counterexamples #normed-spaces #inner-products #topological-vector-spaces
339
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When is a topological vector space “inner product-able”?

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#general-topology #examples-counterexamples #normed-spaces #inner-products #topological-vector-spaces
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Why are weak topologies useful in functional analysis?

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#functional-analysis #topological-vector-spaces #weak-topology
212
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Do algebraically open sets define a vector space topology?

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#functional-analysis #topological-vector-spaces

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