On pairwise k-semi-stratifiable spaces

In this paper, the concept of a pairwise k-semi-stratifiable space is introduced and studied. Some characterizations of pairwise k-semi-stratifiable spaces by means of pairwise g-functions and semi-continuous functions are given. A new characterization of quasi-pseudo-metrizable spaces is obtained by using pairwise k-semi-stratifiable spaces, which improves a theorem of Marín in [17].