近似F-紧空间及其性质  

Nearly F-compact Space and Its Properties

作　　者：陈水利[1] 

机构地区：[1]江汉石油学院基础课部

出　　处：《江汉石油学院学报》1993年第4期83-87,共5页Journal of Jianghan Petroleum Institute

基　　金：国家自然科学基金 编号69075015

摘　　要：建立了近似F-紧空间的概念,给出了近似F-紧性的8个等价条件以及近似F-紧性、几乎F-紧性和NS-闭性之间的关系。同时证明了:①近似F-紧性是正则闭遗传的和有限可和的;②近似F-紧性在不定正则(几乎连续且闭、连续且开等)的Zadeh型函数下保持不变;③对于近似F-紧性而言,Alexander子基引理和Tychonoff乘积定理成立。从而推广了一般拓扑学中的近似紧性和LF拓扑空间中的F-紧性概念。The concept of a nearly F-compact space is established in this paper. Eight equivalent Conditions of the near F-compactness and relationships between near F-compactness. almost F-compactness and NS-closedness are given. Meanwhile, Ⅰ prove that: ①the near F-compactness is regular closed hereditary and finite additive; ②the near F-compactness is preserved under an irresolute regular (almost continuous and closed or continuous and open) Zadeh's type function; ③Alexander's subbase lemma and Tychoff's product theorem are hold for near F-compactness. Thus the notions of near compactness in general topology and F-compactness in LF topological spaces are generalized.

关 键 词：拓扑空间 ZADEH型函数 F紧性 

分 类 号：O159[理学—数学]