集态FU空间的一个注记

A Note on Set-FU Spaces

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： ①A 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.