International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 13, Pages 2081-2093
doi:10.1155/IJMMS.2005.2081
L-fuzzifying topological vector spaces
Cong-Hua Yan1
and Cong-Xin Wu2
1Department of Mathematics, Nanjing Normal University, Jiangsu, Nanjing 210097, China
2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Abstract
The main purpose of this paper is to introduce a concept of L-fuzzifying topological vector spaces (here L is a completely distributive lattice) and study some of their basic properties. Also, a characterization of such spaces in terms of the corresponding L-fuzzifying neighborhood structure of the zero element is given. Finally, the conclusion that the category of L-fuzzifying topological vector spaces is topological over the category of vector spaces is proved.