Real-Valued Functions and Some Covering Properties

DOI：10.3770/j.issn:2095-2651.2016.05.007

 作者 单位 杨二光 安徽工业大学数理学院, 安徽 马鞍山 243032 王力 安徽工业大学数理学院, 安徽 马鞍山 243032

文[1]中定义了性质$(UL)_m^{wl}$, $(UL)_m^K$ 及$(UL)_m$且证明了具有这些性质的空间分别等价于可数仿紧,可数中紧及可数亚紧空间.本文中,我们继续研究由实值函数定义的性质与某些覆盖性质之间的关系,得到可数紧空间及伪紧空间的若干函数刻画.

In the paper [properties defined with semi-continuous functions and some related spaces', {\it Houston J. Math.}, 2015, {\bf 41}(3): 1097--1106] properties $(UL)_m^{wl}$, $(UL)_m^K$ and $(UL)_m$ were defined and it was shown that spaces having these properties coincide with countably paracompact spaces, countably mesocompact spaces and countably metacompact spaces, respectively. In this paper, we continue with the study on the relationship between properties defined with real-valued functions and some covering properties. Some characterizations of countably compact spaces and pseudo-compact spaces in terms of real-valued functions are obtained.