Bounded tightness for locally convex spaces and spaces C(X) |
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Authors: | JC Ferrando |
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Institution: | a Centro de Investigación Operativa, Universidad M. Hernández, E-03202 Elche (Alicante), Spain b Faculty of Mathematics and Informatics, A. Mickiewicz University, 61-614 Poznań, Poland c ETSI Agrónomos (Mathematics) Universidad Politécnica, Camino de Vera s/n, E-46022 Valencia, Spain |
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Abstract: | We show that metrizability and bounded tightness are actually equivalent for a large class of locally convex spaces including (LF)-spaces, (DF)-spaces, the space of distributions D′(Ω), etc. A consequence of this fact is that for the bounded tightness for the weak topology of X is equivalent to the following one: X is linearly homeomorphic to a subspace of . This nicely supplements very recent results of Cascales and Raja. Moreover, we show that a metric space X is separable if the space Cp(X) has bounded tightness. |
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