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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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Extending the Category of Linearly Ordered Spaces
by
Erwin Kronheimer
Birkbeck, London

Write OrdTop for the category of ordered (= totally ordered) sets with a topology - any topology - and weakly order-preserving continuous maps; and, quite illogically, write LinOrdTop for the full subcategory of OrdTop of ordered sets with the usual (``interval'') topology.

Four questions:

What is the smallest full subcategory of OrdTop which contains LinOrdTop and is closed under the construction of

  1. subobjects?

  2. quotient objects?

  3. sub- and quotient objects?

  4. subobjects, quotient objects and inverse limits?

The answer to (1) is - by definition - the category of Cech's ``generalized ordered spaces''. The answer to 2) is the same as to (3). The answer to (4) is simpler (and arguably more interesting) than either, but the proof takes longer.

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-49.