Statistical convergence in topology
type: Item
instance of: scholarly article
title: Statistical convergence in topology
zbMATH Open document ID: 1155.54004
published in: Topology and its Applications
publication date: 2008-12-05T00:00:00Z
review text: The authors introduce and study statistical convergence in topological and uniform spaces and offer some applications to selection principles theory, function spaces and hyperspaces. In section 2 the statistical convergence of a sequence in a topological space is given and related basic properties are studied. Then the idea is considered how statistical convergence can be applied to open covers of topological spaces, and in this connection selection properties related to these covers are handled. Consequently, results concerning uniform selection properties lead us to some interesting applications on function spaces. At last the authors apply the idea of statistical convergence to selection properties on hyperspaces equipped with the so-called delta-topology.
reviewed by: Dieter Leseberg
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 40A30
Mathematics Subject Classification ID: 26A03
Mathematics Subject Classification ID: 11B05
zbMATH DE Number: 5378339
zbMATH Keywords: asymptotic density
zbMATH Keywords: statistical convergence
zbMATH Keywords: statistical limit point
zbMATH Keywords: statistical cluster point
zbMATH Keywords: selection principles
zbMATH Keywords: function spaces
zbMATH Keywords: hyperspaces
author: Giuseppe Di Maio
author: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: j.topol.2008.01.015
OpenAlex ID: W2020003861
cites work: Q5184124
cites work: Q4228099
cites work: Sets of statistical cluster points and \(\mathcal I\)-cluster points
cites work: THE STATISTICAL AND STRONG p-CESARO CONVERGENCE OF SEQUENCES
cites work: R-Type Summability Methods, Cauchy Criteria, P-Sets and Statistical Convergence
cites work: Some covering properties of hyperspaces
cites work: Selection principles and hyperspace topologies
cites work: CONVERGENCE PROPERTIES OF HYPERSPACES
cites work: Uniformizing (proximal) \(\varDelta\)-topologies.
cites work: Q3994935
cites work: Sur Les Densités de Certaines Suites D'Entiers
cites work: Sur la convergence statistique
cites work: Densities and summability
cites work: ON STATISTICAL CONVERGENCE
cites work: Statistical Limit Points
cites work: Tauberian theorems via statistical convergence
cites work: Some approximation theorems via statistical convergence.
cites work: Q3392784
cites work: \(p\)-Fréchet-Urysohn property of function spaces
cites work: Q5515488
cites work: The combinatorics of open covers. II
cites work: Closure properties of function spaces
cites work: Q5421120
cites work: Q5699108
cites work: Q5709184
cites work: Some covering properties in topological and uniform spaces
cites work: Q3542729
cites work: Combinatorics of open covers (VII): Groupability
cites work: \(\mathcal I\)-convergence
cites work: On statistical limit points
cites work: $I$ and $I^*$-convergence in topological spaces
cites work: A Measure Theoretical Subsequence Characterization of Statistical Convergence
cites work: Q4001741
cites work: Q3237217
cites work: Q3878090
cites work: Statistical cluster points and turnpike*
cites work: Superfilters, Ramsey theory, and van der Waerden's theorem
cites work: Combinatorics of open covers. I: Ramsey theory
cites work: Selection principles and covering properties in Topology
cites work: The Integrability of Certain Functions and Related Summability Methods
cites work: Q3425063
cites work: On the Kočinac \(\alpha_i\) properties
DOI: 10.1016/J.TOPOL.2008.01.015
description: scientific article; zbMATH DE number 5378339