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The 12th Summer Conference on General Topology and its Applications
August 12-16, 1997
Nipissing University
North Bay, ON, Canada

Organizers
Ted Chase, Boguslaw Schreyer, Jodi Sutherland, Murat Tuncali, Stephen Watson

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Topologies and bitopologies on totally ordered sets
by
R.D. Kopperman
City College, CUNY
Coauthors: R. G. Wilson (UAM, Iztapalapa, México)

Removing the T1 separation axiom from Cech's axioms for generalized ordered spaces leaves one with arbitrary topologies on totally ordered sets generated by sets of rays (unbounded upper or lower sets); we call these ray topologies. The loss of separation, and in particular, of the symmetry of the specialization order (x <= y <===> x in cl{y}), causes several differences with the traditional theory. We know of two distinct approaches to these differences; one can study totally ordered sets:

  1. with one ray topology, and continuous, order preserving maps, or

  2. with two ray topologies, and with pairwise continuous, order preserving maps.
Two viable theories result. We studied the first of these with E. H. Kronheimer and the second by ourselves. The theories differ considerably, and we report on both.

Date received: July 7, 1997

Copyright © 1997 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 # caao-89.