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Metrizability of $b$-metric space and $��$-metric space via Chittenden's metrization theorem
2019In [An, V.T., Tuyen, Q.L., Dung, V.N., Stone-type theorem on $b$-metric spaces and applications, Topology Appl. 185-186 (2015) 50-64], Tran Van An et al. provide a sufficient condition for $b$-metric space to be metrizable. They proved the metrizability by assuming that the distance function is continuous in one variable.
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Some metrization problem on $$\nu $$-generalized metric spaces
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018Very recently, Dung and Hang (Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, https://doi.org/10.1007/s13398-017-0425-4 , 2017) gave a sufficient condition for some metrization problem on $$\nu $$
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2013
The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. The presentation is self-contained with complet, detailed proofs, and a large number of examples and counterexamples are provided.
Marius Mitrea +3 more
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The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. The presentation is self-contained with complet, detailed proofs, and a large number of examples and counterexamples are provided.
Marius Mitrea +3 more
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Metrizability of Quasi-Metric Spaces
Journal of the London Mathematical Society, 1977T. G. Raghavan, Ivan L. Reilly
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Metrizability of partial metric spaces
Topology and its Applications, 2022Volodymyr Mykhaylyuk, Vadym Myronyk
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A GENERAL RESULT ON METRIZABILITY OF CONE METRIC SPACES
JP Journal of Fixed Point Theory and Applications, 2015Shuwen Xiang, Shunyou Xia
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Spaces metrizable with a Montel metric
Summary: A topology space is called \(M\)-metrizable if it has a metric with the Montel property: every bounded set is relatively compact. This note presents some characterizations (including an embedding theorem) and many other properties of \(M\)-metrizable spaces.Murdeshwar, M. G., Naimpally, S. A.
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Metrization problem of probabilistic metric spaces with applications
The metrization problem is of fundamental importance in the theory and applications of probabilistic metric spaces. The authors introduce the concepts of C-type probabilistic metric space and C-type probabilistic normed linear space. Based on these concepts the metrization problem of such kinds of spaces is considered.Zhang, Shisheng, Kang, Shikun
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On the Macías-Segovia metrization of quasi-metric spaces
Summary: The authors give a direct proof of a theorem of \textit{R. A. Macías} and \textit{C. Segovia} [Adv. Math. 33, 257-270 (1979; Zbl 0431.46018)] on the metrization \((X,\rho)\) of quasi-metric spaces \((X,d)\) without an explicit use of the uniform structure on \(X\times X\).Aimar, Hugo +2 more
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