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Applied General Topology
Universidad Politécnica de Valencia
Volume 2, No. 2, 2001
pp. 119--154 |
Coreflectively modified continuous duality applied to classical product theorems
Frédéric Mynard
Several (old and new) results on stability of quotients (of various types)
under product, on sequentiality of product of sequential spaces, on
relationships between a 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.
2000 Mathematics Subject Classification: 54A05 54A20 54B10 54B15 54B20 54B30 54C10 54C35 54D20 54D45 54D50
54D55 54H12 06B35 06F30 18A05 18B30 18D15
Keywords: Product topology and product maps; Quotient, hereditarily quotient,
countably biquotient, biquotient maps; Sequential, strongly sequential,
Fr\'echet, strongly Fr\'echet topology; Convergence, product convergence,
Antoine convergence, continuous convergence; Cartesian-closedness,
exponential objects
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