Manifolds

Abstract

Vector space is already a large category of topological spaces. However, due to its linear structure, it is already too narrow for many applications in physics. Indeed, the topological and analytic structure is uniquely defined from a neighborhood of the origin alone. Manifold, on the one hand, is a generalization of metrizable vector space, maintaining only the local structure of the latter. On the other hand, every manifold can be considered as a (in general non-linear) subset of some vector space. © 2010 Springer-Verlag Berlin Heidelberg.