NONSTANDARD COMPLETION OF NON-COMPLETE METRIC SPACE
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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