Closed surface

In mathematics a closed surface (2-manifold) is a closed manifold of dimension two, with a single connected component. Examples are spaces like the sphere, the torus, and the Klein bottle. They are classified by the genus and their orientability.

Examples of non-closed surfaces are: an open disk, which is a sphere with a puncture; a cylinder, which is a sphere with two punctures; and the Möbius strip. Manifolds with boundary, compact and of dimension two, also may be classified: by the genus, orientability and the number of boundary circles.

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