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

Received 5 January 2005; Revised 28 May 2005

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.