International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 12, Pages 707-720
doi:10.1155/S0161171202202355

Transitivity in uniform approach theory

Y. J. Lee1 and B. Windels2

1Department of Mathematics, Yonsei University, Seoul 120-749, Korea
2Department of Mathematics and Computer Science, RUCA, University of Antwerp, Groenenborgerlaan 171, Antwerp 2020, Belgium

Received 26 February 2002

Copyright © 2002 Y. J. Lee and B. Windels. 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

We introduce a notion of transitivity for approach uniformities and approach uniform convergence spaces, yielding reflective subconstructs of AUnif and AUCS. Further, we investigate how these new categories are related to uACHY, uACHY U , and uMET, and we show that these relationships are similar to those in the classical case.