Pseudo fuzzy topological (Krasner) hypervector spaces

In this paper, hyper vector spaces, in the sense of Krasner have been studied andVector (pseudo) fuzzy topological hypervector spaces have been introduced, as a generalization of them. In a fuzzy (quasi-)topological hypervector space, we show every its quotient hypervector space by a sub-hypervector space, is again a fuzzy (quasi-)topological hypervector space, and we will discuss its properties.Finally, we introduce the product of two fuzzy quasi-topological hypervector spaces on a specific hyperfield, and show that the product of two fuzzy quasi-topological hypervector spaces is a fuzzy quasi-topological hypervector spaces.Finally, we obtain some important properties of these topological fuzzy topological hypervector spaces.In this paper, hyper vector spaces, in the sense of Krasner have been studied andVector (pseudo) fuzzy topological hypervector spaces have been introduced, as a generalization of them. In a fuzzy (quasi-)topological hypervector space, we show every its quotient hypervector space by a sub-hypervector space, is again a fuzzy (quasi-)topological hypervector space, and we will discuss its properties.Finally, we introduce the product of two fuzzy quasi-topological hypervector spaces on a specific hyperfield, and show that the product of two fuzzy quasi-topological hypervector spaces is a fuzzy quasi-topological hypervector spaces.Finally, we obtain some important properties of these topological fuzzy topological hypervector spaces.