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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 Link to this page: http://www.veryprime.com/dict/orientable_surface.php |