Unbounded Vectorial Cauchy Completion of Vector Metric Spaces

Year 2020, , 761 - 765, 01.09.2020

Çetin Cemal Özeken Cüneyt Çevik

https://doi.org/10.35378/gujs.604784

Cited By: 2

Abstract

A sequence (a_n) in a Riesz space E is called uo-convergent (or unbounded order convergent) to a in E if  inf{|a_n-a|,u} is order convergent to 0 for all u in E₊ and
unbounded order Cauchy (uo-Cauchy) if |a_n-a_n+p|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.

Keywords

Unbounded order convergence, vector metric spaces, unbounded vectorial convergence, unbounded Cauchy completion, Riesz space

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