Compact and bounded sets in intuitionistic fuzzy metric spaces

EFE H., Alaca C.

Demonstratio Mathematica, vol.40, no.2, pp.449-456, 2007 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 2
  • Publication Date: 2007
  • Journal Name: Demonstratio Mathematica
  • Journal Indexes: Scopus
  • Page Numbers: pp.449-456
  • Keywords: Intuitionistic fuzzy metric space, Q-boundedness, Semiboundedness, Totally boundedness, Uniform space
  • Ondokuz Mayıs University Affiliated: No

Abstract

The purpose of this paper is to define q-bounded, semi-bounded, totally bounded, and unbounded sets in an intuitionistic fuzzy metric space X and study the relation between F-bounded sets and the above mentioned sets and prove that the statements (a) X is compact (b) X is sequentially compact and (c) X is complete and totally bounded are all equivalent in an intuitionistic fuzzy metric space X.