$\beta-$connectedness in $L-$topological spaces

Abstract

In this paper, a new kind of connectivity called $\beta-$connectedness in $L-$topological spaces is introduced by means of $\beta-$closed $L-$sets. Some fundamental properties of $\beta-$connectedness are obtained. Especially, the famous K.Fan's Theorem can be extended to $L-$topological spaces for $\beta-$connectedness.