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- W1985887395 abstract "For a given ideal I⊆P(ω), IC(I) denotes the class of separable metric spaces X such that whenever fn:X→R is a sequence of continuous functions convergent to zero with respect to the ideal I then there exists a set of integers {m0<m1<⋯} from the dual filter F(I) such that limi→∞fmi(x)=0 for all x∈X. We prove that for the most interesting ideals I, IC(I) contains only singular spaces. For example, if I=Id is the asymptotic density zero ideal, all IC(Id) spaces are perfectly meager while if I=Ib is the bounded ideal then IC(Ib) spaces are σ-sets." @default.
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- W1985887395 date "2006-12-01" @default.
- W1985887395 modified "2023-09-27" @default.
- W1985887395 title "Ideal convergence of continuous functions" @default.
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- W1985887395 doi "https://doi.org/10.1016/j.topol.2006.03.007" @default.
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