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17th "Summer" Conference on Topology and Applications
July 1-4, 2002
University of Auckland
Auckland, New Zealand

Organizers
David Gauld (University of Auckland), Sina Greenwood (University of Auckland), David McIntyre (University of Auckland), Warren Moors (Waikato University), Sidney Morris (University of South Australia), Vladimir Pestov (Victoria University Wellington), Ivan Reilly (University of Auckland), Des Robbie (University of Melbourne)

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Duality in convergence theory
by
Szymon Dolecki
Burgundy University
Coauthors: F. Mynard (University of Mississippi)

It is shown that to every concrete reflective property P, there corresponds a coreflective property P* so that a convergence is P* if and only if its upper Kuratowski convergence is P. Because the Sierpinski topology is initially dense in the category of all topologies, every continuous convergence (on maps valued in a topological space) is the initial object with respect to upper Kuratowski convergences. Therefore if a convergence is P*, then its continuous convergence (valued in a topological space) is P. Several examples of this duality will be presented.

Date received: June 26, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cait-63.