International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 23, Pages 3781-3797

Completely regular fuzzifying topological spaces

A. K. Katsaras

Department of Mathematics, School of Natural Sciences, University of Ioannina, Ioannina 45110, Greece

Received 24 March 2005; Revised 22 September 2005

Copyright © 2005 A. K. Katsaras. 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.


Some of the properties of the completely regular fuzzifying topological spaces are investigated. It is shown that a fuzzifying topology τ is completely regular if and only if it is induced by some fuzzy uniformity or equivalently by some fuzzifying proximity. Also, τ is completely regular if and only if it is generated by a family of probabilistic pseudometrics.