$P_{Z}(S)$-Metrics and $P_{Z}(S)$-Metric Spaces

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.