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

Ordered compactifications and families of maps

D. M. Liu and D. C. Kent

 Department of Pure and Applied Mathematics, Washington State University, Pullman 99163-3113, WA, USA
Received 28 April 1995; Revised 2 June 1995

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.