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.