International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 13, Pages 2081-2093
-fuzzifying topological vector spaces
1Department of Mathematics, Nanjing Normal University, Jiangsu, Nanjing 210097, China
2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Received 5 January 2005; Revised 28 May 2005
Copyright © 2005 Cong-Hua Yan and Cong-Xin Wu. 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.
The main purpose of this paper is to introduce a concept of
-fuzzifying topological vector spaces (here is a completely
distributive lattice) and study some of their basic properties.
Also, a characterization of such spaces in terms of the
corresponding -fuzzifying neighborhood structure of the zero
element is given. Finally, the conclusion that the category of
-fuzzifying topological vector spaces is topological over the
category of vector spaces is proved.