International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 14, Pages 703-719
Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia
Received 8 July 2003
Copyright © 2004 T. M. G. Ahsanullah and Fawzi Al-Thukair. 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.
We generalize min-neighborhood groups to arbitrary
-neighborhood groups, where 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 -neighborhood group is
-uniformizable, therefore, -completely regular. We also
present several results of -neighborhood groups in conjunction
with -groups due to J. N. Mordeson.