Here is the first two sentences of the first chapter, first section. > A topological n-manifold is a space M locally homeomorphic to R^n. That is, there is a c

Here is the first two sentences of the first chapter, first section. > A topological n-manifold is a space M locally homeomorphic to R^n. That is, there is a cover U = {U_{alpha}} of M by open sets along with maps \phi_{\alpha} : U_{\alpha} -> R^n that are continuous bijections onto their images with continuous inverses.