Topology Proceedings
Document # baal-22
Topology Proceedings 26 No. 1 (2001-2002), pp. 283-296 |
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When are compact, countably compact and Lindelöf convergences topological?
Frédéric Mynard
Conditions on compact convergences to be topological are
(and have been) investigated. New variants are obtained for both filter
and cover compact-like properties such as countable compactness and
Lindelöfness. The recently developed coreflectively modified continuous
duality plays a crucial role in this quest. In particular, the results on
compactness evoked above can be obtained either as byproducts of theorems
on commutation of reflectors with product or as corollaries of internal
characterizations of bireflective subcategories of convergences
determined by coreflectively modified biduals. Both approaches lead to
results of interest for their own.
Keywords: c-embedded spaces, convergence space, continuous convergence,
coreflectively modified bidual, (countable) compactness, Lindelöfness
Mathematics Subject Classification: 54A20 54B30 18B99
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Topology Proceedings,
Volume 26 No. 1 (2001-2002)
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Date: November 1, 2002.