Formally, a topological manifold can be a topological space locally homeomorphic to a Euclidean space. Which means each point incorporates a neighbourhood for which there exists a homeomorphism (a bijective steady operate whose inverse is also ongoing) mapping that neighbourhood to Rn. These homeomorphisms are the charts of your manifold. http://toggle-valve13445.educationalimpactblog.com/12040183/manifold-valve-an-overview