Metric spaces are cone metric spaces, and cone metric spaces are TVS-cone metric spaces. We prove that TVS-cone metric spaces are paracompact. A metrization theorem of TVS-cone metric spaces is obtained by a purely topological tools. We obtain that a homeomorphism f of a compact space is expansive if and only if f is TVS-cone expansive. In the end, for a TVS-cone metric topology, a concrete metric generating the topology is constructed.
Available online xxxx MSC: 40A05 54A20 54E35 54E45 54E50Every metric space is a cone metric space, and every cone metric space is a topological space. In this paper, we introduce and investigate statistical convergence in cone metric spaces, discuss statistically-sequentially compact spaces and characterize statistical completeness of cone metric spaces.
In the paper, necessary and sufficient conditions for two Hausdorff fuzzy metric spaces to be homeomorphic are studied. Also, several properties of the Hausdorff fuzzy metric spaces, as Fboundedness, separability and connectedness are explored.
In this paper, some characterizations for the quasi-metrizability of bispaces are given by means of pairwise weak base-functions, which generalizes some metrization theorems for topological spaces.
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