Categories of topological ordered and bitopological k-spaces.
by
Ralph Kopperman
City College of New York.
Coauthors: J. D. Lawson (Louisiana State University)

Categories of topological ordered and bitopological k-spaces. Abstract: A Cartesian closed category (loosely) is one which has products and function spaces, which behave like those for sets (eg. A^B×C =~ (A^B)^C). Such categories are important in studying computability. The class of k-spaces (in which a set is open if its intersection with each compact subspace is relatively open), is a well-known Cartesian closed topological category.

We find categories of bitopological spaces and of Nachbin topological ordered spaces, which correspond to this classical category of k-spaces. These two categories are isomorphic to each other, via the functor which takes each topological ordered space to the associated bitopological space whose topologies are, respectively, the topologies of upper and lower open sets, and which takes each map into itself. Further, they essentially contain the category of k-spaces whose compact subspaces are Hausdorff; in a way we discuss, its objects are their symmetric objects.

Date received: June 15, 1999

Copyright © 1999 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 # cacl-78.