Unbounded Vectorial Cauchy Completion of Vector Metric Spaces

ÖZEKEN Ç. C., ÇEVİK C.

Gazi University Journal of Science, vol.33, no.3, pp.761-765, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.35378/gujs.604784
  • Journal Name: Gazi University Journal of Science
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, Metadex, Civil Engineering Abstracts, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.761-765
  • Keywords: Unbounded order convergence, Vector metric spaces, Unbounded vectorial convergence, Unbounded Cauchy completion, Riesz space, CONVERGENCE
  • Gazi University Affiliated: Yes

Abstract

A sequence (a(n)) in a Riesz space E is called uo-convergent (or unbounded order convergent) to a is an element of E if vertical bar a(n) - a vertical bar Lambda u -> 0 for all u is an element of E+ and unbounded order Cauchy (uo-Cauchy) if vertical bar a(n) - a(n+p)vertical bar is uo-convergent to 0. In the first part of this study we define u(d,E)-convergence (or unbounded vectorial convergence) in vector metric spaces, which is more general than usual metric spaces, and examine relations between unbounded order convergence, unbounded vectorial convergence, vectorial convergence and order convergence. In the last part we construct the unbounded Cauchy completion of vector metric spaces by the motivation of the fact that every metric space has Cauchy completion. In this way, we have obtained a more general completion of vector metric spaces.