A generalization of ϰ-metrizable spaces

Abstract

We introduce a new class of ϰ-metrizable spaces, namely countably ϰ-metrizable spaces. We show that the class of all ϰ-metrizable spaces is a proper subclass of countably ϰ-metrizable spaces. On the other hand, for pseudocompact spaces the new class coincides with ϰ-metrizable spaces. We prove a generalization of Chigogidze's result that the Čech-Stone compactification of a pseudocompact countably ϰ-metrizable space is ϰ-metrizable.