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International Conference on Applicable General Topology
August 12-18, 2001
Hacettepe University
Ankara, Turkey

Organizers
L. M. Brown (Ankara), G. Brümmer (Cape Town), M. Diker (Ankara), M. Henriksen (Claremont), R. D. Kopperman (New York), G. M. Reed (Oxford), I. L. Reilly (Auckland), S. Salbany (Pretoria), D. Spreen (Siegen)

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Cartesian closedness and extensionality in Top and Cls: a comparison
by
Veerle Claes
Vrije Universiteit Brussel
Coauthors: E. Colebunders, G. Sonck

The construct Cls is the supercategory of Top with objects sets, structured by a possibly non-additive closure operator, and with morphisms, the continuous functions. In our talk, we will elaborate some consequences of the fact that in Top and Cls, both topological categories, the products are formed in a different way. We will compare cartesian closedness and extensionality for both categories. Both categories are not cartesian closed, but for different reasons. In Cls, products do not distribute over coproducts, while for Top, products of quotients are not quotients. With respect to extentionality, Top and Cls behave in a similar way. Finally we will look at the topological universe hull of both categories.

Date received: July 19, 2001

Copyright © 2001 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 # cagx-46.