In this paper, a class of spaces,
called semi-stratifiable spaces is introduced. This class of spaces lies between the class
of semi-metric spaces and the class of spaces in which closed sets are Gδ. This
class of spaces is invariant with respect to taking countable products, closed
maps, and closed unions. In a semi-stratifiable space, bicompactness and
countable compactness are equivalent properties. A semi-stratifiable space is
Fσ-screenable.
A T1-space is semi-metric if and only if it is semi-stratifiable and first countable.
A completely regular space is a Moore space if and only if it is a semi-stratifiable
p-space.
