Tensor Analysis on Differentiable Manifolds

Abstract

We will begin by briefly defining an N-dimensional differentiable manifold M. (See [23, 38, 56, 130].) There are a few assumptions in this definition. A set with a topology is one in which open subsets are known. Furthermore, if for every two distinct elements (or points) p and q there exist open and disjoint subsets containing p and q, respectively, then the topology is called Hausdorff. A connected Hausdorff manifold is paracompact if and only if it has a countable basis of open sets. (See [1, 130, 132].)