Main Article Content
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.