Real-Valued Functions and Some Covering Properties

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.