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International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 105-110
http://dx.doi.org/10.1155/S016117129700015X

Ordered compactifications and families of maps

Department of Pure and Applied Mathematics, Washington State University, Pullman 99163-3113, WA, USA

Received 28 April 1995; Revised 2 June 1995

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For a T3.5-ordered space, certain families of maps are designated as “defining families.“ For each such defining family we construct the smallest T2-ordered compactification such that each member of the family can be extended to the compactification space. Each defining family also generates a quasi-uniformity on the space whose bicompletion produces the same T2-ordered compactification.