实值函数与某些覆盖性质

Real-Valued Functions and Some Covering Properties

中文关键词:  实值函数  数紧空间  伪紧空间  函数插入定理

英文关键词:real-valued functions  countably compact spaces  pseudo-compact spaces  insertion theorems

中文摘要:

      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.

英文摘要:

      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.