摘要
定义了预拓扑空间的邻域系、开邻域基与基;研究了邻域系和开邻域基的性质;给出了两个开邻域基算子彼此等价的充分必要条件以及两个预拓扑基彼此等价的充分必要条件;讨论了预拓扑空间的可数基的一些性质;证明了有限预拓扑有最小基并给出了求最小基的3种算法.
The notions of neighbourhood system, open neighbourhood bases and bases of a pre-topological space are defined. Properties of neighbourhood system and open neighbourhood bases are investigated. Necessary and sufficient conditions for two open neighbourhood base operators to be equivalent, necessary and sufficient conditions for two bases of pre-topological spaces to be equivalent are given. Properties of countable bases of pre-topologicalspaces are also discussed. It is proved that every finite pre-topology has the smallest base,three algorithms to obtain the smallest base are also given.
出处
《纺织高校基础科学学报》
CAS
2008年第1期17-20,共4页
Basic Sciences Journal of Textile Universities
基金
国家自然科学基金资助项目(10271069)
关键词
邻域系
开邻域基
最小基
正交基
基
neighbourhood system
open neighbourhood base ； smallest base ； orthogonal base ； base
