on the topological equivalence of some generalized metric spaces

The aim of this paper is to establish the equivalence between the concepts of an s-metric space and a cone s-metric space using some topological approaches. we introduce a new notion of a tv s-cone s-metric space using some facts about topological vector spaces. we see that the known results on cone s-metric spaces (or n -cone metric spaces) can be directly obtained from the studies on s-metric spaces.