The tangent bundle on $C^1$ fuzzy manifolds

Abstract

Let X be a $C^1$ fuzzy manifold and p be a point in X. At first, it is given that the tangent space at p denoted by $T_p(X)$ is a vector space. In this paper, constructing the tangent bundle $T(X) = V_{pin X} T_p (X)$ on X, it is shown that there is a covariant functor from the category of $C^1$ fuzzy manifolds and fuzzy differentiable functions to the category of the tangent bundles on $C^1$ fuzzy manifolds and fuzzy manifold derivative functions.