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15
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Alternative characterizations of the strong topology in a normed linear space

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#general-topology #continuity #normed-spaces #topological-vector-spaces #dual-spaces
219
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How to show $X := \bigcup_{n \in \mathbb{N}}X_n$ is a locally convex space.

Published on
#functional-analysis #topological-vector-spaces #locally-convex-spaces
96
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Prove that $\{x\in \Bbb{R^n} :\;f(x)\leq k\}$ is compact

Published on
#general-topology #metric-spaces #topological-vector-spaces
552
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Prove that there exists a continuous function $f:E\to \Bbb{R}$ such that $f(x)=1$ if $x\in A$ and $f(x)=0$ if $x\in B.$

Published on
#general-topology #metric-spaces #topological-vector-spaces
192
Views

continuity for TVS

Published on
#functional-analysis #topological-vector-spaces
99
Views

Vector space with the finite topology

Published on
#topological-vector-spaces
65
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Can two ellipsoids meet in a pair of ellipses intersecting in four points?

Published on
#linear-algebra #geometry #geometric-topology #topological-vector-spaces
167
Views

When does the continuous dual of the weak operator topology consist only of finite linear combinations of evaluations?

Published on
#functional-analysis #operator-theory #operator-algebras #topological-vector-spaces #weak-topology
75
Views

Isolated point of a separable F-space

Published on
#functional-analysis #topological-vector-spaces
75
Views

On duality for certain topological vector spaces

Published on
#linear-algebra #topological-vector-spaces
689
Views

Dual basis of Banach spaces?

Published on
#functional-analysis #banach-spaces #topological-vector-spaces
92
Views

Show a directed set of semi-norms on a vector space makes it a topological vector space?

Published on
#general-topology #functional-analysis #analysis #vector-spaces #topological-vector-spaces
422
Views

The definition of the addition is continuous on a linear space with a topology?

Published on
#general-topology #functional-analysis #topological-vector-spaces
438
Views

To show the two metrics induce the same topology but only one of them is complete

Published on
#real-analysis #functional-analysis #metric-spaces #normed-spaces #topological-vector-spaces
415
Views

My proof that the closure of a linear subspace of a topological vector space is again linear.

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

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