Unbounded Vectorial Cauchy Completion of Vector Metric Spaces

Authors : Çetin Cemal ÖZEKEN, Cüneyt ÇEVİK

Pages : 761-765

Doi:10.35378/gujs.604784

View : 18 | Download : 7

Publication Date : 2020-09-01

Article Type : Research Paper

Abstract :A sequence insert ignore into journalissuearticles values( a n ); in a Riesz space E is called uo-convergent insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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