Abstract:The main purpose of this paper is to establish general conditions under which $T_2$-spaces are compact-covering images of metric spaces by using the concept of $cfp$-covers. We generalize a series of results on compact-covering open images and sequence-covering quotient images of metric spaces, and correct some mapping characterizations of $g$-metrizable spaces by compact-covering $\sigma $-maps and $mssc$-maps.
Keywords: $cfp$-covers, compact-covering maps, metrizable spaces, $g$-metrizable spaces, $\sigma $-maps, $mssc$-maps
AMS Subject Classification: 54E40, 54E18, 54C10