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

T-neighborhood groups

Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia

Received 8 July 2003

Copyright © 2004 Hindawi Publishing Corporation. 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 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.