Ideal convergence of bounded sequences

DOI10.2178/jsl/1185803621zbMath1123.40002OpenAlexW2044930053MaRDI QIDQ5294023

Nikodem Mrożek, Ireneusz Recław, Piotr Szuca, Rafał Filipów

Publication date: 9 July 2007

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2178/jsl/1185803621

zbMATH Keywords

ideal convergenceP-pointBolzano-Weierstrass propertyanalytic idealP-idealstatistical densityBolzano-Weierstrass theorem

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Foundations: limits and generalizations, elementary topology of the line (26A03)

Related Items (41)

The Borel complexity of ideal limit points ⋮ On the relationship between ideal cluster points and ideal limit points ⋮ Ideal invariant injections ⋮ $\omega $-diagonalizability of $F_\sigma $ filters ⋮ Unnamed Item ⋮ DENSITY-LIKE AND GENERALIZED DENSITY IDEALS ⋮ Characterizing existence of certain ultrafilters ⋮ On Hindman spaces and the Bolzano-Weierstrass property ⋮ On matrix summability of spliced sequences and \(A\)-density of points ⋮ The ideal test for the divergence of a series ⋮ Characterizations of ideal cluster points ⋮ Splitting positive sets ⋮ Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations ⋮ Unboring ideals ⋮ On some properties of Lévy vectors and their variations ⋮ Banach spaces of \(\mathcal{I} \)-convergent sequences ⋮ Ideal convergent subsequences and rearrangements for divergent sequences of functions ⋮ Qualitative properties of ideal convergent subsequences and rearrangements ⋮ A convergence theorem for the Birkhoff integral ⋮ Convergence in van der Waerden and Hindman spaces ⋮ On nonatomic submeasures on \(\mathbb N\). II ⋮ Extendability to summable ideals ⋮ Ideal version of Egorov's theorem for analytic P-ideals ⋮ Generalized kinds of density and the associated ideals ⋮ \(\mathcal I^{\mathcal K}\)-Cauchy functions ⋮ Different kinds of density ideals ⋮ Solid sequence \(F\)-spaces of \(L_{0}\)-type over submeasures on \(\mathbb N\) ⋮ \(\ell\)-selection principles for sequences of functions ⋮ Density versions of Schur's theorem for ideals generated by submeasures ⋮ Ideals of nowhere dense sets in some topologies on positive integers ⋮ On \(\mathcal{I}\)-neighborhood spaces and \(\mathcal{I}\)-quotient spaces ⋮ On the uniqueness of \(\mathcal{I}\)-limits of sequences ⋮ Limit points of subsequences ⋮ Differentially compact spaces ⋮ Rearrangement of conditionally convergent series on a small set ⋮ Ideal version of Ramsey’s theorem ⋮ On extendability to \(F_\sigma\) ideals ⋮ On spliced sequences and the density of points with respect to a matrix constructed by using a weight function ⋮ Ideal versions of the Bolzano-Weierstrass property ⋮ Mad families, P+(I)-ideals and ideal convergence ⋮ On IA-density of points and some of its consequences

Cites Work

• Homogeneity problems in the theory of Cech compactifications
• Analytic ideals and their applications
• Generalized statistical convergence and convergence free spaces
• Van der Waerden spaces
• Hindman spaces
• Separation Properties of Ideals Over ω
• Combinatorics of dense subsets of the rationals

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