Surface - Closed Surfaces

Closed Surfaces

A closed surface is a surface that is compact and without boundary. Examples are spaces like the sphere, the torus and the Klein bottle. 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.

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Closed Surfaces - Proof
... The classification of closed surfaces has been known since the 1860s, and today a number of proofs exist ... proof of the classification is (Seifert Threlfall 1934), which brings every triangulated surface to a standard form ... This was originally proven only for Riemann surfaces in the 1880s and 1900s by Felix Klein, Paul Koebe, and Henri Poincaré ...

Famous quotes containing the words surfaces and/or closed:

    Footnotes are the finer-suckered surfaces that allow tentacular paragraphs to hold fast to the wider reality of the library.
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