On some BK spaces.
In normed linear space settings, modifying the sequential definition of continuity of an operator by replacing the usual limit "" with arbitrary linear regular summability methods we consider the notion of a generalized continuity (-continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces.
Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.