Statistical convergence in topology
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.
scientific article; zbMATH DE number 5378339
scientific article