Manifold

A manifold is a topological space that locally resembles Euclidean space near each point.

As defined in Physics #

An N-dimensional manifold of points is one for which N independent real coordinates (x1,x2,…,xN) are required to specify a point completely. These N coordinates are denoted collectively by xa, where it is understood that a=1,2,…,N.

As an example, in R2 we have a 2-dimensional manifold of points descrived by the real coordinates (x1,x2).