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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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A link between two notions of connectedness
by
David Holgate
University of Stellenbosch
Coauthors: Gabriele Castellini (University of Puerto Rico, Mayagüez)

A link between two notions of connectedness

Gabriele Castellini and David Holgate*

University of Puerto Rico and University of Stellenbosch

Initiated by Preuß([3-5]), general theories of topological connectedness have been widely studied. Two independent approaches have employed the use of categorical closure operators in the study of connectedness, but until now there has been no link between these two (cf. [1] and [2]).

In this talk we introduce a simple Galois connection that exposes a duality between these two studies. In the process we expand on the ideas presented in [2] and give new insight into the approach taken in [1]. Examples will be given.

References

[1] G. Castellini, ``Connectedness, disconnectedness and closure operators, a more general approach, '' Proceedings of the workshop on categorical topology (L'Aquila, 1994), Kluwer Academic Publishers (1996), 129-138.

[2] M. M. Clementino, W. Tholen, ``Separation versus connectedness, '' Topology and its Appl. 75 (1997), 143-181.

[3] G. Preuß, ``Eine Galois-Korrespondenz in der Topologie, '' Monatsh. Math. 75 (1971), 447-452.

[4] G. Preuß, ``Relative connectednesses and disconnectednesses in topological categories, '' Quaestiones Mathematicae 2 (1977), 297-306.

[5] G. Preuß, ``Connection properties in topological categories and related topics, '' Springer L.N.M. 719 (1979), 293-305.

Date received: June 4, 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-10.