关于L-半拓扑空间中连续性和分离性的探究  

An Exploration of Continuity and Separateness on L-Semi-Topology Space

作　　者：李飞[1] 朱培勇[1] LI Fei;ZHU Peiyong(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]电子科技大学数学科学院,成都611731

出　　处：《四川轻化工大学学报（自然科学版）》2020年第4期89-94,共6页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学青年基金(11501391)。

摘　　要：首先对L-半拓扑空间中的基本点集进行讨论,在L-半拓扑空间中得到了关于子空间的两个结果,并且通过反例证明了在拓扑空间中成立而在L-半拓扑空间中不成立的关于开集的一个命题;然后讨论L-半拓扑空间中映射的连续性,获得了连续映射复合仍连续这一结果,并且证明了L-半拓扑空间中邻域、内点、闭包都具有L-半拓扑不变性;最后,对分离性质进行讨论,在L-半拓扑空间中推广了拓扑空间中关于T0、T1、T2以及正则与正规的一些结果,同时也给出了在拓扑空间中成立而在L-半拓扑空间中不成立的两个例子。Firstly,the basic point set in L-semi-topology space is discussed,two results about subspaces are obtained in L-semi-topology space,and a proposition about open sets that is true in topological space but not true in L-semi-topology space is illustrated by counter-example.Then,the continuity of mapping in L-semi-topology space is discussed,and the result that continuous mapping composition is still continuous is obtained,and it is proved that the neighborhood,inner point and closure in L-semi-topology space all have L-semi-topological invariance.Finally,the separation property is discussed,some results about T 0,T 1,T 2 and regular and normal in L-semi-topology spaces are generalized,and two examples that are true in L-semi-topology spaces but not true in L-semi-topology spaces are also given.

关 键 词：L-半拓扑 L-连续 L-T0空间 L-T1空间 L-T2空间 

分 类 号：O189.11[理学—数学]