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On some BK spaces.

De Malafosse, Bruno (2003)

International Journal of Mathematics and Mathematical Sciences

On some consequences of a generalized continuity

Pratulananda Das, Ekrem Savaş (2014)

Archivum Mathematicum

In normed linear space settings, modifying the sequential definition of continuity of an operator by replacing the usual limit " lim " with arbitrary linear regular summability methods 𝐆 we consider the notion of a generalized continuity ( ( 𝐆 1 , 𝐆 2 ) -continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces.

On spaces with the ideal convergence property

Jakub Jasinski, Ireneusz Recław (2008)

Colloquium Mathematicae

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 I b , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.

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