  In this paper, we define notions of $P_{Z}(S)$-metric and $P_{Z}(S)$-metric
space and we show that every $P_{Z}(S)$-metric Space, analogous to an ordinary
metric space and generally, a $\Lambda$-metric space, is a topological space,
and in continuance, we show that from a topological point of view, some
properties of $P_{Z}(S)$-metric spaces, and $\Lambda$-metric spaces, have
coordination.
