Abstract:Every semi-stratifiable space or strong $\Sigma $-space has a $\sigma $-cushioned (mod$k$)-network. In this paper it is showed that every space with a $\sigma $-cushioned (mod$k$)-network is a D-space, which is a common generalization of some results about D-spaces.
Keywords: D-spaces, (mod$k$)-networks, cushioned collections, semi-stratifiable spaces
AMS Subject Classification: 54E18, 54D20