预拓扑空间的强连通性与局部强连通性  

Strong connectedness and local strong connectedness of pre-topological spaces

作　　者：黄永艳[1] 汪义瑞[2] 田苏妹[1] 李生刚[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]安康学院数学系,陕西安康725000

出　　处：《纺织高校基础科学学报》2011年第2期175-179,共5页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(11071151);陕西省自然科学基金资助项目(2010JM1005)

摘　　要：将强连通拓扑空间和局部强连通拓扑空间这2个概念一般化.运用拓扑和范畴论方法研究了强连通预拓扑空间和局部强连通预拓扑空间的一系列性质,证明了局部强连通预拓扑空间和连续映射构成的范畴LSCPS是topological construct.这一推广是合理的.The notions of strong connected topological space and local strong connected topological space were generalized.Properties of such kinds of pre-topological spaces are investigated systematically by using topological and categorical methods.It is proved that LSCPS,the categoy of local strong connected pre-topological spaces and continuous mappings between them,is a topological construct.This kind of generalization is reasonable.

关 键 词：一般化 预拓扑空间 强连通性 局部强连通性 TOPOLOGICAL CONSTRUCT 

分 类 号：O189.1[理学—数学]