Inverse Preservation Of Some Covering Properties And Weak Base G-Functions

In this paper, we discuss the inverse preservation of some covering properties and the characterizations of metrizable spaces in terms of weak base g—functions.In the first part, by using the concept of ασ-paracompact subsets, we give a sufficient condition for a regular inverse image of a paracompact space under a continuous closed mapping to be paracompact. Also, we give the definition of meta-Lindelof mapping, and we show that meta-Lindel(o|¨)f, δθ-refinable and weakly δθ-refinable are inversely preserved under meta-Lindelof mapping. These results generalize the results given by Gao Guoshi, Chen Bisheng and D. Burke.In the second part of this paper, we characterize metrizable spaces in terms of weak base g—functions and obtain some new metrization theorems.