On spaces with the ideal convergence property
Volume 111 / 2008
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.
