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Coreflectively modified continuous duality applied to classical product theorems. (English) Zbl 1007.54008

Author’s abstract: Several (old and new) results on stability of quotients (of various types) under product, on sequentiality of product of sequential spaces, on relationship between topology and the upper Kuratowski convergence on its closed sets are derived from a general mechanism of duality that uses the continuous convergence. Coreflectively modified biduals with respect to the continuous convergence lead to new reflectors which are of fundamental interest in this quest.

MSC:

54B10 Product spaces in general topology
54D55 Sequential spaces
54B30 Categorical methods in general topology
06F30 Ordered topological structures
18B30 Categories of topological spaces and continuous mappings (MSC2010)
18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
54B15 Quotient spaces, decompositions in general topology
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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