Closed surface
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In mathematics a closed surface (2-manifold) is a space like the sphere, the torus, the Klein bottle. They are classified by the genus and their orientability. Formally these are the closed manifolds that are connected and of dimension two.
Examples of non-closed surface are a disk which is a sphere with a puncture, a cylinder a sphere with two punctures and the Möbius strip. The non-closed surfaces are classified by the genus, orientability and the number of boundaries.