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Re: Strings a minumum topology

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Posted by paultrr on September 15, 2003 at 03:36:05:

In Reply to: Re: Strings a minumum topology posted by Mike2 on September 14, 2003 at 18:05:22:

A manifold is a topological space which is locally Euclidean where around every point, there is a neighborhood which is topologically the same as the open unit ball in R^N. In general, any object which is nearly "flat" on small scales is a manifold. As a topological space, a manifold can be compact or noncompact, and connected or disconnected. They can also be bounded and unbounded.

A submanifold is a subset of a manifold which is itself a manifold, but has smaller dimension. For example, the equator of the earth or any sphere is a submanifold. Many common examples of manifolds are submanifolds of Euclidean space. A smooth manifold with a metric is called a Riemannian manifold and you can have submanifolds of these also.

An orbifold is a quotient space of a manifold under the action of a discrete group.

I do not know if that helps any, but yes, when it comes to brane theory in general the dimensions run all the way from zero on up.

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