Statistical convergence in topology

DOI10.1016/j.topol.2008.01.015zbMath1155.54004OpenAlexW2020003861MaRDI QIDQ958500

Ljubiša D. R. Kočinac, Giuseppe Di Maio

Publication date: 5 December 2008

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2008.01.015

zbMATH Keywords

statistical convergenceasymptotic densitystatistical cluster pointhyperspacesfunction spacesselection principlesstatistical limit point

Mathematics Subject Classification ID

Hyperspaces in general topology (54B20) Function spaces in general topology (54C35) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Convergence and divergence of series and sequences (40A05) Convergence and divergence of series and sequences of functions (40A30) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Density, gaps, topology (11B05) Foundations: limits and generalizations, elementary topology of the line (26A03)

Related Items (only showing first 100 items - show all)

A study on statistical versions of convergence of sequences of functions ⋮ \(\phi\)-statistically quasi Cauchy sequences ⋮ Thinnable ideals and invariance of cluster points ⋮ Statistical convergence and measure convergence generated by a single statistical measure ⋮ Invariance of ideal limit points ⋮ On the relationship between ideal cluster points and ideal limit points ⋮ \(G\)-methods, \(G\)-sequential spaces and \(G\)-continuity in topological spaces ⋮ Ideal invariant injections ⋮ A study on convergence and ideal convergence classes ⋮ On certain variations of \(\mathcal{I}\)-Hurewicz property ⋮ Statistical convergence of nets on locally solid Riesz spaces ⋮ Statistically characterized subgroups of the circle. II: Continued fractions ⋮ Statistical convergence of sequences of functions with values in semi-uniform spaces ⋮ Statistical convergence, selection principles and asymptotic analysis ⋮ Vitali type convergence theorems for Banach space valued integrals ⋮ More about the kernel convergence and the ideal convergence ⋮ Lacunary statistical convergence of double sequences and some inclusion results in \(n\)-normed spaces ⋮ Ideal quasi-Cauchy sequences ⋮ Statistical summability through a lacunary sequence in locally solid Riesz spaces ⋮ Some further results on \(\mathcal I\)-\(\gamma\) and \(\mathcal I\)-\(\gamma_k\)-covers ⋮ On \(\lambda\)-statistical convergence in random 2-normed space ⋮ On statistical convergence with respect to power series methods ⋮ All topologies come from a family of 0-1-valued quasi-metrics ⋮ Compactly uniform Bochner integrability of random elements ⋮ A variation on statistical ward continuity ⋮ Characterizations of ideal cluster points ⋮ Ideal QN-spaces ⋮ Statistical compactness ⋮ Abel summability in topological spaces ⋮ Statistical convergence and statistical continuity on locally solid Riesz spaces ⋮ Statistical convergence of sequences of functions in intuitionistic fuzzy normed spaces ⋮ On statistical convergence in cone metric spaces ⋮ \( \mathcal{I} \)-connected spaces and the images of metric spaces ⋮ Statistical convergence through de la Vallée-Poussin mean in locally solid Riesz spaces ⋮ Compactness with ideals ⋮ On \(\Delta \)-quasi-slowly oscillating sequences ⋮ Sequential definitions of connectedness ⋮ Some further results on ideal convergence in topological spaces ⋮ Qualitative properties of ideal convergent subsequences and rearrangements ⋮ \(f\)-statistical convergence on topological modules ⋮ Decomposition of topologies which characterize the upper and lower semicontinuous limits of functions ⋮ The Baire category of subsequences and permutations which preserve limit points ⋮ \(N_\theta\)-ward continuity ⋮ Unnamed Item ⋮ On statistical exhaustiveness ⋮ Unnamed Item ⋮ On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence ⋮ On the ideal convergence of double sequences in locally solid Riesz spaces ⋮ A convergence theorem for the Birkhoff integral ⋮ Statistical convergence in function spaces ⋮ Some topological properties of fuzzy antinormed linear spaces ⋮ \(\mathcal{I}_\lambda\)-double statistical convergence of order \(\alpha\) in topological groups ⋮ On τ–covers using ideals and some of its consequences ⋮ Statistically characterized subgroups of the circle ⋮ On $$\mathcal {I}$$-Statistically Order Pre Cauchy Sequences in Riesz Spaces ⋮ On difference ideal convergence of double sequences in random 2-normed spaces ⋮ On certain generalized versions of groupability ⋮ Some observations on Hurewicz and \(\mathcal{I}\)-Hurewicz property ⋮ Principle \(\mathrm{S}_1(\mathcal{P}, \mathcal{R})\): ideals and functions ⋮ On weak ideal convergence in normed spaces ⋮ Lacunary ideal convergence of multiple sequences in probabilistic normed spaces ⋮ A study of convergences in partially ordered sets ⋮ Certain aspects of ideal convergence in topological spaces ⋮ Strong \(\Gamma\)-statistical convergence in probabilistic normed spaces ⋮ Statistical order convergence and statistically relatively uniform convergence in Riesz spaces ⋮ Generalized kinds of density and the associated ideals ⋮ \(\mathcal I^{\mathcal K}\)-Cauchy functions ⋮ Ideal-convergence classes ⋮ On statistical convergence in quasi-metric spaces ⋮ On statistical measure theory ⋮ On \(I\)-Cauchy nets and completeness ⋮ Ideal convergence characterization of the completion of linear \(n\)-normed spaces ⋮ \(p\)-\(q\)-convergence of sequences of measurable functions ⋮ When \(\mathcal I\)-Cauchy nets in complete uniform spaces are \(\mathcal I\)-convergent ⋮ Double lacunary density and some inclusion results in locally solid Riesz spaces ⋮ Fuzzifying ideal convergence in fuzzifying topological linear spaces ⋮ A Tauberian theorem for ideal statistical convergence ⋮ On statistically sequentially covering maps ⋮ Solution of a general version of Armacost's problem on topologically torsion elements ⋮ On \(\mathcal{I}\)-neighborhood spaces and \(\mathcal{I}\)-quotient spaces ⋮ Statistical convergence in probability for a sequence of~random functions ⋮ On the uniqueness of \(\mathcal{I}\)-limits of sequences ⋮ \(A\)-distributional summability in topological spaces ⋮ The statistically unbounded τ-convergence on locally solid Riesz spaces ⋮ Korovkin-type theorems and their statistical versions in grand Lebesgue spaces ⋮ On statistical convergence of sequences of closed sets in metric spaces ⋮ The absolutely strongly star-Hurewicz property with respect to an ideal ⋮ Summability and Convergence Using Ideals ⋮ Limit points of subsequences ⋮ On star-K-\(\mathcal{I}\)-Hurewicz property ⋮ The degree of roughness ⋮ Vector-valued spaces of multiplier statistically convergent series and uniform convergence ⋮ Unnamed Item ⋮ On topological spaces defined by \(\mathcal{I} \)-convergence ⋮ Approximity of asymmetric metric spaces ⋮ Generalized ideal convergence in probabilistic normed spaces ⋮ Lacunary ideal summability and its applications to approximation theorem ⋮ On ideal summability and a Korovkin type approximation theorem ⋮ Some remarks on open covers and selection principles using ideals ⋮ Lacunary statistical convergence of double sequences in topological groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Selection principles and hyperspace topologies
• Some covering properties of hyperspaces
• Superfilters, Ramsey theory, and van der Waerden's theorem
• Tauberian theorems via statistical convergence
• \(p\)-Fréchet-Urysohn property of function spaces
• Some approximation theorems via statistical convergence.
• Uniformizing (proximal) \(\varDelta\)-topologies.
• Densities and summability
• \(\mathcal I\)-convergence
• Combinatorics of open covers. I: Ramsey theory
• Some covering properties in topological and uniform spaces
• On the Kočinac \(\alpha_i\) properties
• Sets of statistical cluster points and \(\mathcal I\)-cluster points
• The combinatorics of open covers. II
• On statistical limit points
• Statistical Limit Points
• The Integrability of Certain Functions and Related Summability Methods
• $I$ and $I^*$-convergence in topological spaces
• Sur Les Densités de Certaines Suites D'Entiers
• ON STATISTICAL CONVERGENCE
• THE STATISTICAL AND STRONG p-CESARO CONVERGENCE OF SEQUENCES
• R-Type Summability Methods, Cauchy Criteria, P-Sets and Statistical Convergence
• Statistical cluster points and turnpike^*
• Combinatorics of open covers (VII): Groupability
• Closure properties of function spaces
• A Measure Theoretical Subsequence Characterization of Statistical Convergence
• CONVERGENCE PROPERTIES OF HYPERSPACES
• Selection principles and covering properties in Topology
• Sur la convergence statistique

This page was built for publication: Statistical convergence in topology