Manifold

Revision as of 07:46, 6 April 2008 by Shreyas patankar (talk | contribs) (formal terminology)

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 $X$ is said to be a Manifold if and only if

(i)$X$ is Hausdorff

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

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