Ideal convergence of continuous functions |
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Authors: | Jakub Jasinski Ireneusz Rec?aw |
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Institution: | a Mathematics Department, University of Scranton, USA b Institute of Mathematics, University of Gdansk, Poland |
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Abstract: | For a given ideal I⊆P(ω), IC(I) denotes the class of separable metric spaces X such that whenever 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. |
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Keywords: | primary 54C30 03E35 secondary 26A15 40A30 |
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