\(\mathcal I\)-convergence. (English) Zbl 1021.40001

Summary: We introduce and study the concept of \({\mathcal I}\)-convergence of sequences in metric spaces, where \({\mathcal I}\) is an ideal of subsets of the set \(\mathbb{N}\) of positive integers. We extend this concept to \({\mathcal I}\)-convergence of sequences of real functions defined on a metric space and prove some basic properties of these concepts.


40A30 Convergence and divergence of series and sequences of functions
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
40A99 Convergence and divergence of infinite limiting processes
40C15 Function-theoretic methods (including power series methods and semicontinuous methods) for summability