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# Classification of Surfaces

@inproceedings{GEORGE2011ClassificationOS, title={Classification of Surfaces}, author={CHEN HUI GEORGE}, year={2011} }

- Published 2011

The sphere, torus, Klein bottle, and the projective plane are the classical examples of orientable and non-orientable surfaces. As with much of mathematics, it is natural to ask the question: are these all possible surfaces, or, more generally, can we classify all possible surfaces? In this paper, we examine a result originally due to Seifert and Threlfall that all compact surfaces are homeomorphic to the sphere, the connect sum of tori, or the connect sum of projective planes; for this paper… CONTINUE READING