Unbounded Vectorial Cauchy Completion of Vector Metric Spaces

ÖZEKEN Ç. C., ÇEVİK C.

Gazi University Journal of Science, cilt.33, sa.3, ss.761-765, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.35378/gujs.604784
  • Dergi Adı: Gazi University Journal of Science
  • Derginin Tarandığı İndeksler: 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)
  • Sayfa Sayıları: ss.761-765
  • Anahtar Kelimeler: Unbounded order convergence, Vector metric spaces, Unbounded vectorial convergence, Unbounded Cauchy completion, Riesz space, CONVERGENCE
  • Gazi Üniversitesi Adresli: Evet

Özet

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.