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Category theoretical view of \(I\)-cluster and \(I\)-limit points of subsequences. (English) Zbl 1476.40002

Summary: We study the concepts of \(I\)-limit and \(I\)-cluster points of a sequence, where \(I\) is an ideal with the Baire property. We obtain the relationship between \(I\)-limit and \(I\)-cluster points of a subsequence of a given sequence and the set of its classical limit points in the sense of category theory.

MSC:

40A35 Ideal and statistical convergence
28A12 Contents, measures, outer measures, capacities
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