A Note on Quasi-Metrizable Spaces

Yıl 2024, Cilt: 16 Sayı: 1, 143 – 146, 30.06.2024

Aygül Bilgin Hülya Duru

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

Öz

In a previous paper on quasi-uniformizable spaces related to statistical metric spaces it was determined three conditions to obtain a first countable T1-topology. In this paper, we determine two conditions to define a quasi-metrizable topological space. Namely, we determine the conditions to obtain both a quasi-metric and a quasi-uniform topology coincides with a quasi-metrizable topological space.

Anahtar Kelimeler

uniform space, quasi-uniform space, distribution function, distance function, statistical metric space

Kaynakça

• Csaszar, A., Fondements de la Topologie Ge´ne´rale, Akade´miai Kiado´, Budapest, 1960.
• Duru, H., Ilter, S., Bilgin, A., A first countable T1 topology as related to statistical metric spaces, Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, (in press), (2022).
• Fletcher, P., William F.L., Lecture Notes in Pure and Applied Mathematics Quasi-uniform Spaces, CRC Press, 1982.
• Kelley, J.L., General Topology, Springer, 1975.
• Nachbin, L., Sur les espaces uniformes ordonn´es, Comptes Rendus Hebdomadaires des S´eances de l’Aca´emie des Sciences,226(10)(1948), 774–775.
• Pervin, W.J., Quasi-uniformization of topological spaces, Math. Annalen 147(1962), 316–317.
• Schweizer, B., Sklar, A., Thorp, E., The metrization of statistical metric spaces, Pacific Journal of Mathematics, 10(1960), 673–675.

Yıl 2024, Cilt: 16 Sayı: 1, 143 – 146, 30.06.2024

Aygül Bilgin Hülya Duru

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

Öz

Kaynakça

• Csaszar, A., Fondements de la Topologie Ge´ne´rale, Akade´miai Kiado´, Budapest, 1960.
• Duru, H., Ilter, S., Bilgin, A., A first countable T1 topology as related to statistical metric spaces, Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, (in press), (2022).
• Fletcher, P., William F.L., Lecture Notes in Pure and Applied Mathematics Quasi-uniform Spaces, CRC Press, 1982.
• Kelley, J.L., General Topology, Springer, 1975.
• Nachbin, L., Sur les espaces uniformes ordonn´es, Comptes Rendus Hebdomadaires des S´eances de l’Aca´emie des Sciences,226(10)(1948), 774–775.
• Pervin, W.J., Quasi-uniformization of topological spaces, Math. Annalen 147(1962), 316–317.
• Schweizer, B., Sklar, A., Thorp, E., The metrization of statistical metric spaces, Pacific Journal of Mathematics, 10(1960), 673–675.

Toplam 7 adet kaynakça vardır.

Ayrıntılar

Kaynak Göster

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