Ordered compactifications and families of maps - D. M. Liu; D. C. Kent (International Journal of Mathematics and Mathematical Sciences)
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.