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- W2095181512 abstract "For a Tychonoff space X, we denote by Cp(X) the space of all real-valued continuous functions on X with the topology of pointwise convergence. In this paper, we study the κ-Fréchet Urysohn property and the weak Fréchet Urysohn property of Cp(X). Our main results are that (1) Cp(X) is κ-Fréchet Urysohn iff X has property (κ) (i.e. every pairwise disjoint sequence of finite subsets of X has a strongly point-finite subsequence). In particular, if Cp(X) is a Baire space, then it is κ-Fréchet Urysohn; (2) among separable metrizable spaces, every λ-space has property (κ) and every space having property (κ) is always of the first category; (3) every analytic space has the ω-grouping property, hence for every analytic space X, Cp(X) is weakly Fréchet Urysohn." @default.
- W2095181512 created "2016-06-24" @default.
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- W2095181512 date "2006-09-01" @default.
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- W2095181512 title "Two properties of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo stretchy=false>(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math> weaker than the Fréchet Urysohn property" @default.
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- W2095181512 doi "https://doi.org/10.1016/j.topol.2005.11.012" @default.
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