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
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.