International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 3, Pages 163-172
doi:10.1155/S0161171200003331

Completion of a Cauchy space without the T2-restriction on the space

Abstract

A completion of a Cauchy space is obtained without the T2 restriction on the space. This completion enjoys the universal property as well. The class of all Cauchy spaces with a special class of morphisms called s-maps form a subcategory CHY' of CHY. A completion functor is defined for this subcategory. The completion subcategory of CHY' turns out to be a bireflective subcategory of CHY'. This theory is applied to obtain a characterization of Cauchy spaces which allow regular completion.