\(S\)-\(\mathcal{I}\)-convergence of sequences. (English) Zbl 1456.54001
Summary: In this article, we use the notions of a semi-open set and topological ideal, in order to define and study a new variant of the classical concept of convergence of sequences in topological spaces, namely, the \(S\)-\(\mathcal{I}\)-convergence. Some basic properties of \(S\)-\(\mathcal{I}\)-convergent sequences and their preservation under certain types of functions are investigated. Also, we study the notions related to compactness and cluster points by using semi-open sets and ideals. Finally, we explore the \(\mathcal{I}\)-convergence of sequences in the cartesian product space.
MSC:
| 54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
Keywords:
\(\mathcal{I}\)-convergence; semi-open sets; \(S\)-\(\mathcal{I}\)-convergence; semi-closure; semi-compactness; semicontinuous function; irresolute functionReferences:
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