International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 92870, 8 pages

Dimension theory and fuzzy topological spaces

S. S. Benchalli, B. M. Ittanagi, and P. G. Patil

Department of Mathematics, Karnatak University, Dharwad 580003, Karnataka, India

Received 27 September 2005; Revised 10 May 2006; Accepted 30 May 2006

Copyright © 2006 S. S. Benchalli et al. 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.


J. M. Aarts introduced and studied a new dimension function, Hind, in 1975 and obtained several results on this function. In this paper, a new local inductive dimension function called local huge inductive dimension function denoted by locHind is introduced and studied. Furthermore, an effort is made to introduce and study dimension functions for fuzzy topological spaces. It has been possible to introduce and study the small inductive dimension function indfX and large inductive dimension function indfX for a fuzzy topological space X.