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The Eleventh Summer Conference on General Topology and Applications
August 10-13, 1995
University of Southern Maine
Gorham, ME, USA

Organizers
J. Baumgartner, D. Briggs, J. deBakker, B. Flagg, G. Gruenhage, M. Guay, Y. Kong, R. Kopperman, S. Shore, J. Rutten, J. Vaughan

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Connectedness and Disconnectedness in Bitopological Spaces
by
Harriet M. Lord
Cal Poly at Pomona

Definition. Let A be a class of bitopological spaces.

C(A) = {(X, T1, T2) | f:(X, T1, T2) --> (A, S1, S2) is constant whenever f is bicontinuous and (A, S1, S2) in A}.

D(B) = {(Y, S1, S2) | f:(X, T1, T2) --> (A, S1, S2) is constant whenever f is bicontinuous and (X, T1, T2) in B}.

If A = D(C(A)), A is called a disconnectedness, and if B = C(D(B)), then B is called a connectedness.

The above definitions were motivated by the fact that a topological space X is connected if and only if every continuous map into 2D, the two-point discrete space, must be constant. In addition, a topological space Y is totally disconnected if and only if every continuous map from a connected space to Y must be constant.

We present connectednesses and disconnectednesses induced by various bitopological structures on a two-point set, and show that all but finitely many classes of disconnectednesses consist of bitopological spaces in which both topologies are T1.

Date received: April 12, 1996

Copyright © 1996 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 # caae-54.