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15
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What do we call a Schauder-like basis that is uncountable?

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#terminology #topological-vector-spaces #schauder-basis
127
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How to prove in a topological vector space in R^n: cl(A) + cl(B) =cl(clA+clB), where cl denotes closure and A, B compact convex sets?

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#general-topology #functional-analysis #topological-vector-spaces
190
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Give an example of Euclidean space.

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#topological-vector-spaces #orthonormal
430
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Prove that a set is dense and of the first category in $L^2(T)$

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#general-topology #functional-analysis #topological-vector-spaces #baire-category
90
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Is there a non-complete and non-separate metric space?

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#metric-spaces #topological-vector-spaces
770
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Extending continuous, densely-defined linear maps between locally convex spaces

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#functional-analysis #topological-vector-spaces #locally-convex-spaces
94
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Is there a topological space and meanwhile a linear space such that its vector addition is discontinuous but scalar multiplication is continuous?

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#differential-topology #topological-vector-spaces
1.8k
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Is Reflexivity Necessary for the Weak and Weak* Topologies to Coincide?

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#functional-analysis #topological-vector-spaces
163
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Two basic questions about topological linear space theory

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#topological-vector-spaces
1.1k
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Given a Banach space $X$, are weak$^*$ bounded subsets of the dual space $X '$ also strongly bounded (with respect to the usual norm in $X '$)?

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#functional-analysis #banach-spaces #topological-vector-spaces
930
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Weak* continuity

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#functional-analysis #measure-theory #normed-spaces #topological-vector-spaces
342
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When does a dense subspace destine the weak topology?

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#general-topology #functional-analysis #topological-vector-spaces #locally-convex-spaces
194
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Closed Monoidal Structures On The Category Of Complete Topological Vector Spaces

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#functional-analysis #category-theory #topological-vector-spaces
132
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$\sigma$-Algebra: Why do we want it to contain complements as well?

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#measure-theory #topological-vector-spaces
1k
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Why do we need dual space

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#functional-analysis #soft-question #vector-spaces #topological-vector-spaces

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