Reflexive extended locally convex spaces (Q6607328)

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scientific article; zbMATH DE number 7915149
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Reflexive extended locally convex spaces
scientific article; zbMATH DE number 7915149

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    Reflexive extended locally convex spaces (English)
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    18 September 2024
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    The authors continue their investigation of extended locally convex spaces (elcs) in the sense of \textit{D.~Salas} and \textit{S.~Tapia-García} [Topology Appl. 210, 317--354 (2016; Zbl 1359.46003)]. Here, they use the topology \(\tau_{ucb}\) of uniform convergence on bounded subsets of an elcs \((X,\tau)\) to explore its reflexivity property. In particular, they show that an elcs is (semi) reflexive if and only if its open subspaces are (semi) reflexive. Moreover, it is shown that reflexivity of extended normed spaces is a three-space property.
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    extended locally convex space
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    extended normed space
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    topology of uniform convergence
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    reflexive spaces
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    three-space property
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