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A First Countable T1 Topology as related to Statistical Metric Spaces

Cilt: 28 Sayı: 1 30 Nisan 2023
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A First Countable T1 Topology as related to Statistical Metric Spaces

Öz

In this paper, we study the conditions under which one can obtain a first countable and 𝑇1 topology without the left-continuity and symmetry, which have an important role in the statistical metric space theory.

Anahtar Kelimeler

Quasi-metric, Quasi-uniformity, Statistical metric space

Kaynakça

  1. Bilgin, A. (2021). Olasılıksal metrik uzaylar ile kuazi-düzgün uzaylar arasındaki bazı ilişkiler. (MS), Istanbul University, Institute of Science Istanbul, Turkey.
  2. Császár, Á. (1960). Fondements de la Topologie Générale. Budapest, Hungary: Akadémiai Kiadó.
  3. Fletcher, P. & William F. L. (1982). Lecture notes in pure and applied mathematics quasi-uniform Spaces. New York, USA: CRC Press. doi:10.1201/9780203741443
  4. Kelley, J. L. (1975). General Topology. New York, USA: Springer-Verlag.
  5. Krishnan, V. S. (1955). A note on semi-uniform spaces. Journal of Madras University Section B, 25, 123-124.
  6. Menger, K. (1942). Statistical metrics. Proceedings of the National Academy of Sciences, 28(12), 535-537. doi:10.1073/pnas.28.12.535
  7. Pervin W.J., (1962). Quasi-uniformization of topological Spaces. Mathematische Annalen, 147, 316-317.
  8. Schweizer, B. & Sklar, A. (1960). Statistical metric spaces. Pacific Journal of Mathematics, 10(4), 313-334.
  9. Schweizer, B., Sklar, A., & Thorp, E. (1960). The metrization of statistical metric spaces. Pacific Journal of Mathematics, 10(4), 673 - 675.
  10. Schweizer, B., & Sklar, A. (1983). Probabilistic Metric Spaces. New York, USA: Elsevier Science Publishing Co., Inc.

Kaynak Göster

APA
Duru, H., İlter, S., & Bilgin, A. (2023). A First Countable T1 Topology as related to Statistical Metric Spaces. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 28(1), 285-289. https://doi.org/10.53433/yyufbed.1168520
AMA
1.Duru H, İlter S, Bilgin A. A First Countable T1 Topology as related to Statistical Metric Spaces. YYUFBED. 2023;28(1):285-289. doi:10.53433/yyufbed.1168520
Chicago
Duru, Hülya, Serkan İlter, ve Aygül Bilgin. 2023. “A First Countable T1 Topology as related to Statistical Metric Spaces”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28 (1): 285-89. https://doi.org/10.53433/yyufbed.1168520.
EndNote
Duru H, İlter S, Bilgin A (01 Nisan 2023) A First Countable T1 Topology as related to Statistical Metric Spaces. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28 1 285–289.
IEEE
[1]H. Duru, S. İlter, ve A. Bilgin, “A First Countable T1 Topology as related to Statistical Metric Spaces”, YYUFBED, c. 28, sy 1, ss. 285–289, Nis. 2023, doi: 10.53433/yyufbed.1168520.
ISNAD
Duru, Hülya - İlter, Serkan - Bilgin, Aygül. “A First Countable T1 Topology as related to Statistical Metric Spaces”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 28/1 (01 Nisan 2023): 285-289. https://doi.org/10.53433/yyufbed.1168520.
JAMA
1.Duru H, İlter S, Bilgin A. A First Countable T1 Topology as related to Statistical Metric Spaces. YYUFBED. 2023;28:285–289.
MLA
Duru, Hülya, vd. “A First Countable T1 Topology as related to Statistical Metric Spaces”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 28, sy 1, Nisan 2023, ss. 285-9, doi:10.53433/yyufbed.1168520.
Vancouver
1.Hülya Duru, Serkan İlter, Aygül Bilgin. A First Countable T1 Topology as related to Statistical Metric Spaces. YYUFBED. 01 Nisan 2023;28(1):285-9. doi:10.53433/yyufbed.1168520

Cited By

A Note on Quasi-Metrizable Spaces

Turkish Journal of Mathematics and Computer Science

https://doi.org/10.47000/tjmcs.1224591