关于几种著名的广义度规结构的度量化性的注记
Some remarks on the metrizability of some well known generalized metric-like structures
摘要：
在\cite [1，An，V.T.，Tuyen，Q.L.和Dung，V.N.，Stone-type theorem on $b$-度量空间and applications，拓扑应用185 - 186（2015），50 - 64.] {an}An等人给出了$b$-度量空间可度量化的一个充分条件。然而，他们对度量化的证明依赖于一个假设，即距离函数在一个变量中是连续的。在这篇短文中，我们以一种更简化的方式改进了这个结果，而不考虑对距离函数的任何假设。此外，我们还给出了Jleli和Samet最近在\cite [1，Jleli，M.和Samet，B.，关于度量空间的新推广，J.不动点理论应用（2018）20：128]{JS1}。最后，本文给出了Khojasteh等人在\cite [1，Khojasteh，F.，Karapinar，E.和Radenovic，S.，$θ$-度量空间：推广，数学问题工程2013年第504609卷，7页]{ks}。
英文摘要：
In \cite[\, An, V.T., Tuyen, Q.L. and Dung, V.N., Stone-type theorem on $b$-metric spaces and applications, Topology Appl. 185-186 (2015), 50-64.]{an}, An et al. had provided a sufficient condition for $b$-metric spaces to be metrizable. However, their proof of metrizability relied on an assumption that the distance function is continuous in one variable. In this short note, we improve upon this result in a more simplified way without considering any assumption on the distance function. Moreover, we provide two shorter proofs of the metrizability of $\mathcal{F}$-metric spaces recently introduced by Jleli and Samet in \cite[\, Jleli, M. and Samet, B., On a new generalization of metric spaces, J. Fixed Point Theory Appl. (2018) 20:128]{JS1}. Lastly, in this short note, we give an alternative proof of the metrizability of $θ$-metric spaces introduced by Khojasteh et al. in \cite[\, Khojasteh, F., Karapinar, E. and Radenovic, S., $θ$-metric space: A Generalization, Math. Probl. Eng. Volume 2013, Article 504609, 7 pages]{ks}.
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