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On the Set of Locally Convex Topologies Compatible with a Given Topology on a Vector Space: Cardinality Aspects

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Martín Peinador, Elena and Tarieladze, V. (2016) On the Set of Locally Convex Topologies Compatible with a Given Topology on a Vector Space: Cardinality Aspects. Journal of Mathematical Sciences, 216 (4). pp. 577-579. ISSN 10723374

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Official URL: http://link.springer.com/article/10.1007%2Fs10958-016-2917-8



Abstract

For a topological vector space (X, τ ), we consider the family LCT (X, τ ) of all locally convex topologies defined on X, which give rise to the same continuous linear functionals as the original topology τ . We prove that for an infinite-dimensional reflexive Banach space (X, τ ), the cardinality of LCT (X, τ ) is at least c.


Item Type:Article
Subjects:Sciences > Mathematics > Algebra
ID Code:39260
Deposited On:07 Oct 2016 12:06
Last Modified:12 Dec 2018 15:12

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