★-quasi-pseudometrics on algebraic structures

• He, Shi-Yao ^[1] ; Jin, Ying-Ying ^[2] ; Xie, Li-Hong ^[1]
  1. [1] Wuyi University
  2. [2] Guangzhou Panyu Polytechnic
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 24, Nº. 2, 2023, págs. 253-265
• Idioma: inglés
• DOI: 10.4995/agt.2023.19303
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we introduce some concepts of ★-(quasi)-pseudometric spaces, and give an example which shows that there is a ★-quasi-pseudometric space which is not a quasi-pseudometric space. We also study the conditions under which ★-quasi-pseudometric semitopological groups are paratopological groups or topological groups.

• Referencias bibliográficas
  • A. V. Arhangel'skii and M. G. Tkachenko, Topological Groups and Related Structures, Atlantis Press, World Sci., 2008. https://doi.org/10.2991/978-94-91216-35-0
  • N. Brand, Another note on the continuity of the inverse, Arch. Math. 39 (1982), 241-245. https://doi.org/10.1007/BF01899530
  • R. Ellis, A note on the continuity of the inverse, Proc. Amer. Math. Soc 8 (1957), 372-373. https://doi.org/10.1090/S0002-9939-1957-0083681-9
  • A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Syst. 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
  • A. George and P. Veeramani, Some theorems in fuzzy metric spaces, J. Fuzzy Math. 3 (1995), 933-940. https://doi.org/10.1016/0165-0114(94)90162-7
  • A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Syst. 90 (1997), 365-368. https://doi.org/10.1016/S0165-0114(96)00207-2
  • V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Syst. 115 (2000), 485-489. https://doi.org/10.1016/S0165-0114(98)00281-4
  • V. Gregori and S. Romaguera, Fuzzy quasi-metric spaces, Appl. Gen. Topol. 5 (2004), 129-136. https://doi.org/10.4995/agt.2004.2001
  • S. Y. He, L. H. Xie and P.-F. Yan, On ★-metric spaces, Filomat 36, no. 18 (2022), 6173-6185. https://doi.org/10.2298/FIL2218173H
  • I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975), 326-334.
  • S. M. A. Khatami and M. Mirzavaziri, Yet another generalization of the notion of a metric space, arXiv:2009.00943v1 (2020).
  • C. Liu, Metrizability of paratopological (semitopological) groups, Topology Appl. 159 (2012), 1415-1420. https://doi.org/10.1016/j.topol.2012.01.002
  • J. R. Munkres, Topology (2nd Edition), Prentice Hall, New Jersey, 2000.
  • O. V. Ravsky, Paratopological groups I, Mat. Stud. 16 (2001), 37-48.
  • S. Romaguera and M. Sanchis, On fuzzy metric groups, Fuzzy Sets Syst. 124 (2001), 109-115. https://doi.org/10.1016/S0165-0114(00)00085-3
  • I. Sánchez and M. Sanchis, Fuzzy quasi-pseudometrics on algebraic structures, Fuzzy Sets Syst. 330 (2018), 79-86. https://doi.org/10.1016/j.fss.2017.05.022
  • I. Sánchez and M. Sanchis, Complete invariant fuzzy metrics on groups, Fuzzy Sets Syst. (2018), 41-51. https://doi.org/10.1016/j.fss.2016.12.019
  • J. J. Tu and L. H. Xie, Complete invariant fuzzy metrics on semigroups and groups, J. Appl. Anal. Comput. 11 (2020), 766-771. https://doi.org/10.11948/20190394
  • W. Zelazko, A theorem on $B_{0}$ division algebras, Bull. Acad. Pol. Sci. 8 (1960), 373-375.