SI-convergence in \(T_0\) spaces. (English) Zbl 1473.54022
Summary: Recently, H. Andradi et al. [Filomat 32, No. 17, 6017–6029 (2018; https://doi.org/10.2298/FIL1817017A] asked whether one can find a complete characterization of \(T_0\) spaces for the SI-convergence being topological. In this paper, we give a positive answer to this problem. More precisely, we introduce the notion of \(I^\ast \)-continuous spaces, and prove that the SI-convergence in a \(T_0\) space is topological if and only if the \(T_0\) space is \(I^\ast \)-continuous.
MSC:
| 54D10 | Lower separation axioms (\(T_0\)–\(T_3\), etc.) |
| 06B30 | Topological lattices |
| 06B35 | Continuous lattices and posets, applications |
| 54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
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