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Recent development in sequential convergence. (English) Zbl 0567.54002
The purpose of this survey is to report on the development in the theory of sequential convergence spaces since the Fifth Prague Topological Symposium, held in 1981. The authors not only review several recent results, that have mostly the form of examples and counterexamples, but also show that there is a general construction that contains some of these examples as particular cases. The basic idea of this method is to start with an infinite set S and an almost disjoint family \({\mathcal F}\) of infinite subsets of S, to equip the disjoint union \(S\cup {\mathcal F}\) with an appropriately chosen Hausdorff completely regular 0-dimensional topology, and to modify this space into a more complicated one, yielding the desired (counter)example.
Reviewer: C.Nemethi

54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54D55 Sequential spaces
54G20 Counterexamples in general topology