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实值函数与某些覆盖性质
引用本文:杨二光,王力.实值函数与某些覆盖性质[J].数学研究及应用,2016,36(5):561-567.
作者姓名:杨二光  王力
作者单位:安徽工业大学数理学院, 安徽 马鞍山 243032,安徽工业大学数理学院, 安徽 马鞍山 243032
基金项目:国家自然科学基金 (Grant Nos.11401262; 11271178).
摘    要:In the paper properties defined with semi-continuous functions and some related spaces',Houston J.Math.,2015,41(3):1097–1106] properties(U L)~(wl)_m,(U L)~K_m and(U L)_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.

关 键 词:实值函数  数紧空间  伪紧空间  函数插入定理
收稿时间:2015/7/20 0:00:00
修稿时间:2015/10/12 0:00:00

Real-Valued Functions and Some Covering Properties
Erguang YANG and Li WANG.Real-Valued Functions and Some Covering Properties[J].Journal of Mathematical Research with Applications,2016,36(5):561-567.
Authors:Erguang YANG and Li WANG
Institution:School of Mathematics $\&$ Physics, Anhui University of Technology, Anhui 243032, P. R. China and School of Mathematics $\&$ Physics, Anhui University of Technology, Anhui 243032, P. R. China
Abstract: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.
Keywords:real-valued functions  countably compact spaces  pseudo-compact spaces  insertion theorems
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