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
Department of Mathematics, University of Western Australia, Nedlands 6009, WA, Australia
Received 5 April 1999; Revised 27 April 1999
Copyright © 2000 Nandita Rath. 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
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.