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Statistical convergence in topology. (English) Zbl 1155.54004
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.

MSC:
54A20Convergence in general topology
54B20Hyperspaces (general topology)
54C35Function spaces (general topology)
54D20Noncompact covering properties (paracompact, Lindelöf, etc.)
40A05Convergence and divergence of series and sequences
40A30Convergence and divergence of series and sequences of functions
26A03Elementary topology of the real line
11B05Topology etc. of sets of numbers