Suzuki, Tomonari; Alamri, Badriah; Kikkawa, Misako Only 3-generalized metric spaces have a compatible symmetric topology. (English) Zbl 1348.54025 Open Math. 13, 510-517 (2015). Summary: We prove that every 3-generalized metric space is metrizable. We also show that for any \(v\) with \(v\geq 4\), not every \(v\)-generalized metric space has a compatible symmetric topology. Cited in 1 ReviewCited in 10 Documents MSC: 54E99 Topological spaces with richer structures Keywords:\(v\)-generalized metric space; metrizability; topology; symmetrizable; semimetrizable PDFBibTeX XMLCite \textit{T. Suzuki} et al., Open Math. 13, 510--517 (2015; Zbl 1348.54025) Full Text: DOI References: [1] [1] B. Alamri, T. Suzuki and L. A. Khan, Caristi’s fixed point theorem and Subrahmanyam’s fixed point theorem in ʋ-generalized metric spaces, J. Funct. Spaces, 2015, Art. ID 709391, 6 pp.; · Zbl 1321.54055 [2] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31-37. MR1771669; · Zbl 0963.54031 [3] G. Gruenhage, “Generalized metric spaces” in Handbook of set-theoretic topology, 1984, pp. 423-501, North-Holland, Amsterdam. MR0776629; [4] Z. Kadelburg and S. Radenovi´c, On generalized metric spaces: A survey, TWMS J. Pure Appl. Math., 5 (2014), 3-13.; · Zbl 1305.54040 [5] W. A. Kirk and N. Shahzad, Generalized metrics and Caristi’s theorem, Fixed Point Theory Appl., 2013, 2013:129. MR3068651; · Zbl 1295.54060 [6] T. Suzuki, Generalized metric spaces do not have the compatible topology, Abstr. Appl. Anal., 2014, Art. ID 458098, 5 pp.; · Zbl 1470.54017 [7] S. Willard, General Topology, Dover (2004). MR2048350; · Zbl 1052.54001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.