Shu-Ping Li - Department of Computer Science and Technology, Mudanjiang Teachers College, Mudanjiang, Heilongjiang ۱۵۷۰۱۲, P.R. China
Zheng Fang - Department of Computer Science and Technology, Daqing Teachers College, Daqing, Heilongjiang ۱۵۷۰۱۲, P.R. China
Jie Zhao - Department of Computer Science and Technology, Mudanjiang Teachers College, Mudanjiang, Heilongjiang ۱۵۷۰۱۲, P.R. China

In this paper, a certain new connectedness of L-fuzzy subsets inL-topological spaces is introduced and studied by means of preclosed sets. Itpreserves some fundamental properties of connected set in general topology.Especially the famous K. Fan’s Theorem holds.

L-topological space, Preclosed set, P-connected set, P۲-connected set