Some new results of completion t^ω- Normed approach space

Abstract

In this paper , the completion of t^ω-approach spaces, isometric in t^ω-approach space and equivalent sequences are defined. Every t^ω-approach normed space can be embedded in t^ω-approach Banach space is proved, χ ̃ and an isometry ψ from χ onto the subspace F of χ ̃ which is dense in χ ̃ are introduced, as well as, the completion is shown an uniquely up to an isometry. In addition, to what is mentioned above, some essential definitions, examples, and important theorems are included to illustrate some of our work.