A Note on Quasi-Metrizable Spaces

Author:

Bilgin Aygül1ORCID,Duru Hülya2ORCID

Affiliation:

1. HALİÇ ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ

2. İSTANBUL ÜNİVERSİTESİ, FEN FAKÜLTESİ

Abstract

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.

Publisher

Turkish Journal of Mathematics and Computer Science, Association of Mathematicians

Reference7 articles.

1. Csaszar, A., Fondements de la Topologie Ge´ne´rale, Akade´miai Kiado´, Budapest, 1960.

2. 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).

3. Fletcher, P., William F.L., Lecture Notes in Pure and Applied Mathematics Quasi-uniform Spaces, CRC Press, 1982.

4. Kelley, J.L., General Topology, Springer, 1975.

5. 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.

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