The Banach manifold C(M,N)

Abstract

Let M be a compact manifold without boundary and let N be a connected manifold without boundary. For each k is an element of N the set of k times continuously differentiable maps between M and N has the structure of a smooth Banach manifold where the underlying manifold topology is the compact-open C-k topology. We provide a detailed and rigorous proof for this important statement which is already partially covered by existing literature. (C) 2019 Elsevier B.V. All rights reserved.