1Mathematics Department University of Scranton Scranton, PA 18510-4666, U.S.A. 2Institute of Mathematics University of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland
Colloquium Mathematicum, Tome 111 (2008) no. 1, pp. 43-50
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.
Keywords:
subseteq omega ideal continue investigation class spaces i ideal convergence property denoted mathcal analytic non countably generated p ideal mathcal subseteq addition non pathological isomorphic mathcal spaces have measure zero present characterization mathcal spaces using clopen covers
Affiliations des auteurs :
Jakub Jasinski
1
;
Ireneusz Rec/law
2
1
Mathematics Department University of Scranton Scranton, PA 18510-4666, U.S.A.
2
Institute of Mathematics University of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland
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Jakub Jasinski; Ireneusz Rec/law. On spaces with the ideal convergence property. Colloquium Mathematicum, Tome 111 (2008) no. 1, pp. 43-50. doi: 10.4064/cm111-1-4
