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orientable surface
Author: Marian Olejar, Jr. Created: Sep/25/2006 Last edit: Oct/05/2006

    topology:
    The closed orientable surfaces are the sphere (`S_0`), the torus (`S_1`), the double torus (`S_2`), the triple torus (`S_3`), ... generally `S_g` where g is a genus.
    
    Each one of closed orientable surfaces can be obtained by adding some handles to a sphere in 3D space.
    
    Every closed connected orientable surface is homeomorphic to one of `S_0, S_1, ...`.
    
    graph theory:
    Every (finite) graph G can be drawn without edge-crossings on some closed surfaces, if we first draw components of G without edge-crossings and then add each handle for each edge-crossing.

See also:
nonorientable surface,

Cite this article as:
Marian Olejar, Jr.: orientable surface from VeryPrime's Dictionary of mathematics
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