A+ CATEGORY SCIENTIFIC UNIT

On spaces with the ideal convergence property

Volume 111 / 2008

Jakub Jasinski, Ireneusz Rec/law Colloquium Mathematicum 111 (2008), 43-50 MSC: Primary 54C30, 03E35; Secondary 26A15, 40A30. DOI: 10.4064/cm111-1-4

Abstract

Let $I\subseteq P(\omega)$ be an ideal$.$ We continue our investigation of the class of spaces with the $I$-ideal convergence property, denoted $\mathcal{IC}(I)$. We show that if $I$ is an analytic, non-countably generated $P$-ideal then $\mathcal{IC}(I)\subseteq s_{0}.$ If in addition $I$ is non-pathological and not isomorphic to $I_{b},$ then $\mathcal{IC}(I)$ spaces have measure zero. We also present a characterization of the $\mathcal{IC}(I)$ spaces using clopen covers.

Authors

  • Jakub JasinskiMathematics Department
    University of Scranton
    Scranton, PA 18510-4666, U.S.A.
    e-mail
  • Ireneusz Rec/lawInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland
    e-mail

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