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Convergence-theoretic approach to quotient quest. (English) Zbl 0862.54001
In topology there are natural relations between various classes of maps on one hand and various properties of topological spaces on the other hand. In particular there are theorems of the following kind: a topological space \(X\) has property \(P\) iff there exists a space \(Y\) with (the usually nicer) property \(Q\) and a special kind of quotient maps \(f:Y\to X\) (e.g., hereditary quotient, bi-quotient, almost open, open). The author investigates corresponding questions in the setting of convergence spaces and provides many interesting results. These generalizations seem particularly appropriate in view of the fact special types of quotient maps in Top are nothing else but categorical quotient maps in categories of suitable convergence spaces [cf. in particular H. L. Bentley, the reviewer and R. Lowen, Res. Expo. Math. 18, 3-20 (1991; Zbl 0753.18002)].

MSC:
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54B15 Quotient spaces, decompositions in general topology
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