NONSTANDARD COMPLETION OF NON-COMPLETE METRIC SPACE

  • Ala Omer Hassan Department of Mathematic, College of Science, Salahaddin University-Erbil, Kurdistan Region, Iraq
  • Ibrahim Othman Hamad Department of Mathematic, College of Science, Salahaddin University-Erbil, Kurdistan Region, Iraq
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 introduce a new notion of completion corresponding to nonstandard modified metric , and to use it to reprove the classical (standard) completion theorem and to overcome the incompetence of those spaces which has deprivation at a small size subset.

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Published
2021-08-18
How to Cite
Hassan, A. and Hamad, I. (2021) “NONSTANDARD COMPLETION OF NON-COMPLETE METRIC SPACE”, Zanco Journal of Pure and Applied Sciences, 33(4), pp. 129-135. doi: 10.21271/ZJPAS.33.4.13.
Section
Mathematics ,Physics and Engineering Researches