Some metrization problem on ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document}-generalized metric spaces

Very 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 ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document}-generalized metric spaces. Strongly motivated by their result, we give sufficient and necessary conditions on the conclusion of their theorem. We also give sufficient and necessary conditions on the assumption of their theorem. Thus we could tell that we almost complete the metrization problem on ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document}-generalized metric spaces with respect to their method.