NONSTANDARD COMPLETION OF NON-COMPLETE METRIC SPACE

Ala O. Hassan; Ibrahim O. Hamad

doi:10.21271/ZJPAS.33.4.13

Authors

Ala O. Hassan Department of Mathematic, College of Science, Salahaddin University-Erbil, Kurdistan Region, Iraq
Ibrahim O. Hamad Department of Mathematic, College of Science, Salahaddin University-Erbil, Kurdistan Region, Iraq

DOI:

https://doi.org/10.21271/ZJPAS.33.4.13

Keywords:

Nonstandard, infinitesimal, completion, unlimited, infinitely close, non-complete spaces.

Abstract

Our aim in this study is to establishing nonstandard foundations, definitions and theorems for completion a noncomplete metric spaces. We have a lot of space or sets X which agree with all usual properties of complete, except at a small size subset of it. In this paper, by using nonstandard analysis tools founded by A. Robinson and axiomatized by E. Nelson, we try to reformulate the definition of completion corresponding to nonstandard modified metric , and to give a nonstandard form to the classical (standard) completion theorem and to use the power of nonstandard tools to overcome the incompetence of those spaces which has deprivation at a small size subset.

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