A note on a theorem of Talagrand |
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| Authors: | S. Moll,L.M. Sá nchez Ruiz |
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| Affiliation: | a Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Valencia, Camino de Vera s/n, Valencia, Spain
b Escuela Técnica Superior de Ingeniería del Diseño, Universidad Politécnica, de Valencia, Camino de Vera s/n, Valencia, Spain |
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| Abstract: | We provide an elementary argument to show that if for a hemicompact kR-space X the space Cp(X) contains a subset S which separates the points of X and is dominated by irrationals, i.e. S is covered by a family  of compact sets such that Kα⊂Kβ for α?β, then Cp(X) is also dominated by irrationals; consequently Cp(X) is K-analytic. This fact (which fails for non-hemicompact spaces X) extends an old result of Talagrand. |
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| Keywords: | 46A50 54D20 54H05 |
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