On countable bounded tightness for spaces Cp(X) |
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Authors: | J. Ka?kol |
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Affiliation: | a Faculty of Mathematics and Informatics, A. Mickiewicz University, Matejki 48-49, 60-769 Poznań, Poland b ETSI Agronomos (Mathematics), E-46071 Valencia, Spain |
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Abstract: | It is well known that the space Cp([0,1]) has countable tightness but it is not Fréchet-Urysohn. Let X be a Cech-complete topological space. We prove that the space Cp(X) of continuous real-valued functions on X endowed with the pointwise topology is Fréchet-Urysohn if and only if Cp(X) has countable bounded tightness, i.e., for every subset A of Cp(X) and every x in the closure of A in Cp(X) there exists a countable and bounding subset of A whose closure contains x. We study also the problem when the weak topology of a locally convex space has countable bounded tightness. Additional results in this direction are provided. |
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Keywords: | Fré chet-Urysohn spaces Monolithic spaces Countable tightness |
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