Monad metrizable space

Creative Commons License

GÖÇÜR O.

Mathematics, vol.8, no.11, pp.1-14, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 11
  • Publication Date: 2020
  • Doi Number: 10.3390/math8111891
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Page Numbers: pp.1-14
  • Keywords: Amply soft monad point, Amply soft set, AS topology, Monad metric space, Monad metrizable space, Parametric separation axioms, PAS metric space, PAS topology, Pi,i = 0, 1, 2, 3, 4, Soft metric space, Soft set theory
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2020 by the author. Licensee MDPI, Basel, Switzerland.Do the topologies of each dimension have to be same and metrizable for metricization of any space? I show that this is not necessary with monad metrizable spaces. For example, a monad metrizable space may have got any indiscrete topologies, discrete topologies, different metric spaces, or any topological spaces in each different dimension. I compute the distance in real space between such topologies. First, the passing points between different topologies is defined and then a monad metric is defined. Then I provide definitions and some properties about monad metrizable spaces and PAS metric spaces. I show that any PAS metric space is also a monad metrizable space. Moreover, some properties and some examples about them are presented.