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First countability, nets and sequences in the weak topology.

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#general-topology #functional-analysis #weak-convergence #locally-convex-spaces
72
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Why is this set $Z$ convex?

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#functional-analysis #distribution-theory #topological-vector-spaces #locally-convex-spaces
1.3k
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Linear Map is injective iff Adjoint has dense image

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#functional-analysis #locally-convex-spaces
565
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If locally convex topologies exhibit the same dual spaces, do they exhibit the same continuous linear operators?

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#general-topology #functional-analysis #operator-theory #topological-vector-spaces #locally-convex-spaces
174
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Application of the separation theorem of convex sets

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#functional-analysis #locally-convex-spaces
104
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Prove limit exists for an almost monotonic bounded function, involves convexity and square integrability

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#real-analysis #limits #lp-spaces #bounded-variation #locally-convex-spaces
36
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Why is $\bigcup\limits_{|c| \leq 1} cU$ convex?

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#real-analysis #topological-vector-spaces #locally-convex-spaces
692
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Mackey–Arens theorem and the weak topology

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#functional-analysis #topological-vector-spaces #locally-convex-spaces
51
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Construct a sequence $(x_{n})$ such that $\bigcap_{n=1}^{\infty} K_{n} = \{x\}$, and $(x_{n})$ is not bounded.

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#functional-analysis #banach-spaces #lp-spaces #locally-convex-spaces
101
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Showing that the balls given by seminorms form a local base

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#functional-analysis #topological-vector-spaces #locally-convex-spaces
42
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Showing $\forall q\in\mathcal{P}_Y$ there exists $ p\in\mathcal{P}_X:q\circ A\le p\implies A:X\to Y$ continuous

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#functional-analysis #topological-vector-spaces #locally-convex-spaces #open-map
72
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$f|_{(a, b)}$ convex. Is $f$ convex on $[a, b]$?

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#real-analysis #convex-analysis #locally-convex-spaces
108
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Closed graph theorem for operator topologies - Do operator topologies yield Fréchet spaces?

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#functional-analysis #operator-theory #operator-algebras #locally-convex-spaces #closed-graph
47
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Derivative of vector-valued functions using duality

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#functional-analysis #derivatives #locally-convex-spaces
65
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Pettis integral on locally convex space and seminorms

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#integration #measure-theory #operator-algebras #topological-vector-spaces #locally-convex-spaces

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