Abstract
Abstract This paper introduces the notion of a C 1 fuzzy manifold as a natural development of the notions of a fuzzy topological vector space and of a fuzzy derivative of a fuzzy continuous mapping between fuzzy topological vector spaces. First, a fuzzy atlas of class C 1 on a set is constructed and shown to yield a fuzzy topology that is compatible with the fuzzy atlas. The structure of a C 1 fuzzy manifold on the set then follows. Next, it is shown that the product of two fuzzy manifolds is a fuzzy manifold, and that the composition of two fuzzy differentiable mappings between fuzzy manifolds is fuzzy differentiable. Finally, the notions of a tangent vector and of a tangent space at a point in a fuzzy manifold are formulated, and the tangent space is shown to be a vector space.
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