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A manifold is an abstraction of Euclidean space, so it hasWhat is the difference between Manifold space to Euclidean space?

What properties does the Manifold space have that Euclidean space doesn't have?

That is, until we add extra properties to a manifold that are not possible in Euclidean space.

A manifold is only locally

It means that a manifold does have angles and distances, but these can change from point to point in a continuous fashion.

As such it allows:

- Curved spaces since the global
*parallel postulate*of Euclidean geometry is not (necessarily) true. - Non-
*orientable*shapes like the*Klein bottle*. - Disconnected components that may even have different dimensions.