[0,1]-拓扑空间中的Starplus-连通性(英文)

STARPLUS-CONNECTEDNESS IN [0,1]-TOPOLOGICAL SPACES

本文在I-拓扑空间中引入Starplus-连通性的概念,并且研究它的性质.借助于水平拓扑,得到了下面结果:Starplus-连通性是一般拓扑学中连通性的好推广而且被连续映射保持.一个Starplus-连通的模糊集一定是O-连通的.另外,模糊单位区间和模糊实直线是Starplus-连通的.

The aim of this paper is to introduce the concept of starplus-connectedness and research its propertis in I-topological spaces. By means of level topology, we obtain the following resuhs： starplus-connectedness is a good extension of connectedness in general topology and it is preserved by a continuous mapping. A starplus-eonnected fuzzy set must be O-connected. Moreover, both the fuzzy unit interval and the fuzzy real line are starplus-eonnected.