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Semi-convergence of filters and nets. (English) Zbl 0970.54003
Summary: In [Am. Math. Mon. 70, 36-41 (1963; Zbl 0113.16304)] N. Levine introduced the concept of semi-open set and semi-continuity. Semi-convergence and semi-compactness were first introduced, investigated and characterized by C. Dorsett in [Ann. Soc. Sci. Brux., Ser. I 92, 143-150 (1978; Zbl 0408.54009)] and [Indian J. Mech. Math. 19, 11-17 (1981; Zbl 0508.54020)], respective1y. In this paper semi-convergence and semi-clusterence of filters are introduced, investigated and characterized.

54A05 Topological spaces and generalizations (closure spaces, etc.)
54C08 Weak and generalized continuity
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)