Real-Valued Functions and Some Covering Properties
Received:July 20, 2015  Revised:October 12, 2015
Key Words: real-valued functions   countably compact spaces   pseudo-compact spaces   insertion theorems
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11401262; 11271178).
 Author Name Affiliation Erguang YANG School of Mathematics $\&$ Physics, Anhui University of Technology, Anhui 243032, P. R. China Li WANG School of Mathematics $\&$ Physics, Anhui University of Technology, Anhui 243032, P. R. China
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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.