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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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http://link.springer.com/article/10.1007%2Fs10958-016-2917-8
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2016
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Springer New York
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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.
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Álgebra
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1201 Álgebra
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1. F. Albiac and N. J. Kalton, Topics in Banach SpaceTheory, Grad. Texts Math., 233, SpringerVerlag, New York (2006). 2. R. Whitley, “Mathematical notes: Projecting m onto c0,” Am. Math. Mon., 73, No. 3, 285–286 (1966). 3. W. Sierpinski, Cardinal and Ordinal Numbers, Monogr. Mat., 34, Panstowe Wydawnictwo Naukowe, Warszawa (1965).
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https://hdl.handle.net/20.500.14352/24630
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