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On Dimension of Hypervector Spaces

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Abstract (2. Language): 
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.
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