The tangent bundle on C1 fuzzy manifolds

Abstract

Let X be a C' fuzzy manifold and p be a point in X. At first, it is given that the tangent space at p denoted by 7'p(^) is a vector space. İn this paper, constructing the tangent bundle nx}= V T(X)on X, it is shown that there is a covariant functor from the category of C' fuzzy manifolds and fuzzy differentiable functions to the category of the tangent bundles on C' fuzzy manifolds and fuzzy manifold derivative functions.

A study on fuzzy tangent bundle of fuzzy Banach manifold

“…Definition 2.9. [7] The mapping φ is said to be tangent at 0 if given a neighborhood Definition 2.10. [5] Let X, Y be two fuzzy topological vector spaces.…”

“…In 2003, Guner has defined the tangent bundle on C 1 fuzzy manifold [7], using their approach we define fuzzy tangent bundle on fuzzy Banach manifold.…”

“…Some of the important developments are Fuzzy Banach Spaces and Fuzzy Metric Spaces which are introduced by many authors namely Bag et al [1,16] and Saadati and Vaezpour [18] in different perception. In 1993, Ferraro and Foster have introduced the concept of C 1 fuzzy manifold [6], and in 2003, Guner introduced tangent bundle on C 1 fuzzy manifold [7], with the similar approach in our previous papers [8,9,10] we have introduced the concept of fuzzy Banach manifold and studied some of its fuzzy topological properties.…”

“…Let M be a fuzzy Banach manifold with fuzzy tangent bundle T(M). A fuzzy tangent norm on M is a fuzzy set on T(M) × (0, ∞), i.e., N :T(M) × (0, ∞) −→ [0, 1] such that for every p ∈ M the restriction N p :T p (M) × (0, ∞) −→ [0, 1]is a fuzzy norm on T p (M) satisfying the following condition of fuzzy norm[7],∀u, v ∈ T p (M), t, s > 0: (1) N (u, t) > 0. (2) N (u, t) = 1 iff u = 0.…”