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

Copyright © 2005 Hindawi Publishing Corporation. 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.

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.