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# All Questions

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### Mackey topology characterising property

Let $V$ be a topological $k$-vector space. Let $V^{\star}$ denote the space of all linear functionals $V \rightarrow k$ and $V' \subset V^{\star}$ the subspace of all continuous linear functionals. ...
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Consider the following setup. Let $K$ be a compact topological space, $X$ a Fréchet space and $T:K \times X \to X$ a continuous family of linear maps (i.e. $T$ is a continuous map and $T_k \equiv T(k, ... 1answer 89 views ### Is the compact-open topology on the dual of a separable Frechet space sequential? Let$X$be a separable Frechet space (= Polish locally convex linear metric space) and$X'_c$be the space of linear continuous functionals on$X$, endowed with the compact-open topology (= the ... 1answer 131 views ### The completeness of spaces of continuous functions with the compact-open topology For a Tychonoff space$X$let$C_k(X)$denote the space of continuous real-valued functions on$X$, endowed with the compact-open topology. Problem. Is the space$C_k(X)$Polish if it is Polishable ... 2answers 209 views ### On convergent sequences in locally convex topological vector spaces Assume that a sequence$(x_n)_{n\in\omega}$of points of a locally convex topological vector space converges to zero. Is it always possible to find increasing number sequences$(n_k)_{k\in\omega}$and ... 1answer 258 views ### Is restriction a closed map? Originally asked on MSE. Let$X$be a normal (or even metrizable) topological space and let$Y$be a closed subset of$X$. Let$C(X)$be the linear space of all continuous scalar functions on$X$... 1answer 110 views ### Compactness of operators and norming sets Originally asked on MSE. Let$T$be a linear map from a normed space$E$into a Banach space$F$. Let$D\subset \overline{B}_{F^{\ast}}$be norming, i.e., there is$r>0$such that$\sup\limits_{v\...

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