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

TL;DR

This paper introduces $P_{Z}(S)$-metric spaces, demonstrating their topological properties and similarities to traditional metric spaces, thereby expanding the understanding of generalized metric structures.

Contribution

The paper defines $P_{Z}(S)$-metric spaces and explores their topological properties, establishing parallels with ordinary and $ ext{Lambda}$-metric spaces.

Findings

$P_{Z}(S)$-metric spaces are topological spaces.

Properties of $P_{Z}(S)$-metric spaces coordinate with those of $ ext{Lambda}$-metric spaces.

The study extends metric space theory to a broader class of spaces.

Abstract

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.