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Displaying similar documents to “Ideal convergence and divergence of nets in ( ℓ ) -groups”

On spaces with the ideal convergence property

Jakub Jasinski, Ireneusz Recław (2008)

Colloquium Mathematicae

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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.

Remarks on statistical and I -convergence of series

Jaroslav Červeňanský, Tibor Šalát, Vladimír Toma (2005)

Mathematica Bohemica

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In this paper we investigate the relationship between the statistical (or generally I -convergence) of a series and the usual convergence of its subseries. We also give a counterexample which shows that Theorem 1 of the paper by B. C. Tripathy “On statistically convergent series”, Punjab. Univ. J. Math. 32 (1999), 1–8, is not correct.

More than a 0-point

Jana Flašková (2006)

Commentationes Mathematicae Universitatis Carolinae

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We construct in ZFC an ultrafilter U ∈ ℕ * such that for every one-to-one function f : ℕ → ℕ there exists U ∈ U with f [ U ] in the summable ideal, i.e. the sum of reciprocals of its elements converges. This strengthens Gryzlov’s result concerning the existence of 0 -points.