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The purpose of this paper is the study of dimension of hypervector spaces.
In this regard first we introduce the notions of linear independent (resp.
dependent) and basis of hypervector spaces. Then we study the properties of hypervector spaces and prove that under certain conditions dimension for
such spaces there exist. Finally, we use the fundamental relation on
hypervector spaces to construct a functor from the category of hypervector
spaces over a fixed field K and the category of classical vector spaces
over K, and we will prove that this functor preserves dimension.