On the topological equivalence of S-metric and cone S-metric spaces

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The aim of this paper is to establish the equivalence between the concepts of an S-metric space and a cone S-metric space usingsome topological approaches. We introduce a new notion of TVS-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.