★-quasi-pseudometrics on algebraic structures

Authors

DOI:

https://doi.org/10.4995/agt.2023.19303

Keywords:

invariant ★-(quasi-)pseudometric, topological group, paratopological groups, topological semigroup

Abstract

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.

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Author Biographies

Shi-Yao He, Wuyi University

School of Mathematics and Computational Science

Ying-Ying Jin, Guangzhou Panyu Polytechnic

Department of General Required Courses

Li-Hong Xie, Wuyi University

School of Mathematics and Computational Science

References

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.

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Published

2023-10-02

How to Cite

[1]
S.-Y. He, Y.-Y. Jin, and L.-H. Xie, “★-quasi-pseudometrics on algebraic structures”, Appl. Gen. Topol., vol. 24, no. 2, pp. 253–265, Oct. 2023.

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Section

Regular Articles