L-拓扑空间的R-强连通性

R-strong connectedness in L-topological space

研究L-拓扑空间中的R-强连通性,运用类比、推广的方法,将一般拓扑空间中的R-强连通性引入到L-拓扑空间中.定义了L-拓扑空间中R-强连通集以及R-强连通L-拓扑空间的概念,证明了L-拓扑空间的R-强连通性具有任意可积性,以及R-强连通性的樊畿定理,得出了R-强连通性是拓扑不变性和L-好的推广等结论.扩展了一般拓扑学中的一些结果.

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.