
Chapter 5 Manifolds, Tangent Spaces, Cotangent Spaces
... a C k -manifold of dimension n consists of a topological space, M , together with an equivalence class, A, of C k n-atlases, on M . Any atlas, A, in the equivalence class A is called a di↵erentiable structure of class C k (and dimension n) on M . We say that M is modeled on Rn. When k = 1, we say th ...
... a C k -manifold of dimension n consists of a topological space, M , together with an equivalence class, A, of C k n-atlases, on M . Any atlas, A, in the equivalence class A is called a di↵erentiable structure of class C k (and dimension n) on M . We say that M is modeled on Rn. When k = 1, we say th ...
Chapter 2: Limits and Continuity
... One-Sided Limits Numbers x near c fall into two natural categories: those that lie to the left of c and those that lie to the right of c. We write ...
... One-Sided Limits Numbers x near c fall into two natural categories: those that lie to the left of c and those that lie to the right of c. We write ...