Ordered compactifications and families of maps

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.

Keywords

• T3.5-ordered space
• T2-ordered compactification
• defining family of maps
• quasi-uniform space
• bicompletion.