R-strong connectedness in L-topological space

The R-strong connectedness in L-topological spaces was studied.The R-strong connectedness in general topological spaces is introduced to L-topological spaces with the help of methods of analogy and generalization.Concepts of R-strong connected set in L-topological spaces and R-strong connected L-topological spaces are difined.It is proved that R-connected L-topological spaces must be connected and the product of a class of R-strong connected L-topological spaces is also R-strong connected.Then,some characteristics of Rstrong connectedness of L-topological spaces are given,and the Ky Fan theorem of R-strong connectedness is proved.Conclusions that R-strong connectedness of L-topological spaces is a topologically invariant property and an L-good extension of R-strong connectedness of general topological spaces are got.Some results of general topology are extended.