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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

1 Issue per year


IMPACT FACTOR 2016 (Open Mathematics): 0.682
IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

CiteScore 2016: 0.62

SCImago Journal Rank (SJR) 2016: 0.454
Source Normalized Impact per Paper (SNIP) 2016: 0.850

Mathematical Citation Quotient (MCQ) 2016: 0.23

Open Access
Online
ISSN
2391-5455
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Volume 13, Issue 1 (Sep 2015)

Issues

Only 3-generalized metric spaces have a compatible symmetric topology

Tomonari Suzuki
  • Department of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan
  • Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Badriah Alamri
  • Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Misako Kikkawa
  • Department of Mathematics, Faculty of Science, Saitama University, Sakura, Saitama 338-8570, Japan
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-09-04 | DOI: https://doi.org/10.1515/math-2015-0048

Abstract

We prove that every 3-generalized metric space is metrizable. We also show that for any ʋ with ʋ ≥ 4, not every ʋ-generalized metric space has a compatible symmetric topology.

Keywords: ʋ-generalized metric space; Metrizability; Topology; Symmetrizable; Semimetrizable

References

  • [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. Web of ScienceGoogle Scholar

  • [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 Google Scholar

  • [3] G. Gruenhage, “Generalized metric spaces” in Handbook of set-theoretic topology, 1984, pp. 423–501, North-Holland, Amsterdam. MR0776629 Google Scholar

  • [4] Z. Kadelburg and S. Radenovi´c, On generalized metric spaces: A survey, TWMS J. Pure Appl. Math., 5 (2014), 3–13. Google Scholar

  • [5] W. A. Kirk and N. Shahzad, Generalized metrics and Caristi’s theorem, Fixed Point Theory Appl., 2013, 2013:129. MR3068651 Web of ScienceGoogle Scholar

  • [6] T. Suzuki, Generalized metric spaces do not have the compatible topology, Abstr. Appl. Anal., 2014, Art. ID 458098, 5 pp. Web of ScienceGoogle Scholar

  • [7] S. Willard, General Topology, Dover (2004). MR2048350 Google Scholar

About the article

Received: 2015-01-27

Accepted: 2015-08-03

Published Online: 2015-09-04


Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0048.

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©2015 Tomonari Suzuki et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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[1]
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[2]
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Fixed Point Theory and Applications, 2017, Volume 2017, Number 1
[3]
Nguyen Van Dung and Vo Thi Le Hang
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017
[4]
Tomonari Suzuki
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017
[5]
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Journal of Inequalities and Applications, 2016, Volume 2016, Number 1

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