Abstract
We used the concept of preopen sets to introduce a particular form of the μ-countability axioms; namely pre-countability axioms, this class of axioms includes; pre-separable spaces, pre-first countable spaces and pre-second countable spaces. In this article, we study the topological properties of these spaces, as the hereditary property and their images by some particular functions; moreover we investigate the behavior of pre-countability axioms in some special spaces as; submaximal spaces, regular spaces and partition spaces