International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 14, Pages 703-719
doi:10.1155/S0161171204307052

T-neighborhood groups

T. M. G. Ahsanullah and Fawzi Al-Thukair

 Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia
Received 8 July 2003

Abstract

We generalize min-neighborhood groups to arbitrary T-neighborhood groups, where T is a continuous triangular norm. In particular, we point out that our results accommodate the previous theory on min-neighborhood groups due to T. M. G. Ahsanullah. We show that every T-neighborhood group is T-uniformizable, therefore, T-completely regular. We also present several results of T-neighborhood groups in conjunction with TI-groups due to J. N. Mordeson.