Only 3-generalized metric spaces have a compatible symmetric topology

• Autorzy: Tomonari Suzuki , Badriah Alamri , Misako Kikkawa
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-01-27

zaakceptowano

2015-08-03

online

2015-09-04

Twórcy

autor

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

autor

Badriah Alamri

• Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

autor

Misako Kikkawa

• Department of Mathematics, Faculty of Science, Saitama University, Sakura, Saitama 338-8570, Japan

Bibliografia

• [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. [WoS]
• [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
• [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.
• [5] W. A. Kirk and N. Shahzad, Generalized metrics and Caristi’s theorem, Fixed Point Theory Appl., 2013, 2013:129. MR3068651 [WoS]
• [6] T. Suzuki, Generalized metric spaces do not have the compatible topology, Abstr. Appl. Anal., 2014, Art. ID 458098, 5 pp. [WoS]
• [7] S. Willard, General Topology, Dover (2004). MR2048350

Identyfikatory

DOI

10.1515/math-2015-0048