Kostyrko, Pavel; Šalát, Tibor; Wilczyński, Władysław \(\mathcal I\)-convergence. (English) Zbl 1021.40001 Real Anal. Exch. 26(2000-2001), No. 2, 669-685 (2001). 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. Cited in 27 ReviewsCited in 207 Documents MSC: 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 Keywords:ideals of sets; Baire classification of functions; statistical convergence; metric spaces PDFBibTeX XMLCite \textit{P. Kostyrko} et al., Real Anal. Exch. 26, No. 2, 669--685 (2001; Zbl 1021.40001)