A New Type of Topological Vector space Via t^ω Approach Structure

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Maysoon A. Neamah, Boushra Y. Hussein


The major aim of this work is to introduce the connotation of  - approach topological vector space, which is an protraction of  - topological vector space. In this paper, we clarify  the relation between metric space and an approach space, we define - contraction function and prove many new properties and exist some results, furthermore, we define -  approach group and introduce some examples in the - approach group. We describe the - approach subgroup and find the relation between - topological space and - approach space. We give the important and adequate condition to get - approach topological space. Finally, we define - approach vector space, - approach subspace, and - topological vector space.

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