On 2S-metric spaces

ÇETKİN V., GÜNER E., AYGÜN H.

SOFT COMPUTING, vol.24, no.17, pp.12731-12742, 2020 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 17
  • Publication Date: 2020
  • Doi Number: 10.1007/s00500-020-05134-w
  • Journal Name: SOFT COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Page Numbers: pp.12731-12742
  • Keywords: Soft set, Soft point, 2-metric, Soft 2-metric, Metric topology, Completeness, SOFT SET-THEORY, THEOREM
  • Kocaeli University Affiliated: Yes

Abstract

In this paper, we introduce 2-metric spaces in terms of soft points, called 2s-metric spaces, in the soft universe, which is a nonlinear generalization of soft metric spaces. Then we induce a soft topology from a given 2s-metric space and also study some of its topological structures such as open balls, open (closed) sets, completeness and etc. After that, we prove the Cantor's Intersection Theorem for complete 2s-metric spaces and use it to show that such a space cannot be expressed as a countable union of no-where dense soft sets under some general situations. At the end, we obtain some fixed point results in complete 2s-metric spaces by using Cantor's theorem.