Manifold

A manifold is a topological space locally homeomorphic to an open ball in some Euclidean space. The Whitney embedding theorem allows us to visualise manifolds as being 'embedded' in some Euclidean space.

Definition

A Topological space is said to be a Manifold if and only if

(i) is Hausdorff

(ii) is second-countable, i.e. it has a countable base.