集态FU空间的一个注记

集态FU空间的一个注记 A Note on Set-FU Spaces 王汉锋 WANG Hanfeng1 1 first-author 李仁所 LI Rensuo1 1 李进金 LI Jinjin2 2 山东农业大学数学系 山东农业大学数学系 Department of Mathematics,Shandong Agriculture University,Taian Department of Mathematics,Shandong Agriculture University,Taian 漳州师范学院数学系 漳州师范学院数学系 Department of Mathematics,Zhangzhou Normal College Department of Mathematics,Zhangzhou Normal College 集态FU空间是由Arhangel’skii引入的一类弱第一可数空间.本文讨论了强集态FU空间、集态FU空间以及弱FU空间之间的关系:①具有可数紧度的集态FU空间是强集态FU空间;②利用紧集列给出了强集态FU空间成为弱FU空间的一个充分条件.给出了集态FU空间的一个映射性质:集态FU空间被有限到一、满的连续闭映射所保持与逆保持. A set-FU space is a special class of weakly first countable spaces introduced by Arhangel’skii.In this paper,we investigate the relationship between strong set-FU spaces,set-FU spaces and weak FU-spaces as follows: ① A set-FU space with countable tightness is a strong set-FU space;② A sufficient condition for strong set-FU spaces being weak FU-spaces is given by compact set sequences.A mapping property for set-FU spaces is given: set-FU spaces are preserved and adversely preserved by a finite-to-one,closed,continuous and onto mapping. 集态FU空间 弱FU空间 可数紧度 闭映射 set-FU spaces weakly FU spaces countable tightness closed mapping 10.14188/j.1671-8836.2011.02.018 O189.1 国家自然科学基金资助项目（10971186）;山东省科技厅科技发展计划项目（J08LI09） 2011-02-01 2021-04-01 2 57