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Covering Space
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Geliefert zwischen Mi., 28.01.2026 und Do., 29.01.2026
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High Quality Content by WIKIPEDIA articles! In mathematics, more specifically algebraic topology, a covering map is a continuous surjective function p a from a topological space, C, to a topological space, X, such that each point in X has a neighbourhood evenly covered by p. This means that for each point x in X, there is associated an ordered pair, (K, U), where U is a neighborhood of x and where K is a collection of disjoint open sets in C, each of which gets mapped homeomorphically, via p, to U (as shown in the image). In particular, this means that every covering map is necessarily a local homeomorphism. Under this definition, C is called the covering space of X. Covering spaces also play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. For example: In Riemannian geometry, ramification is a generalization of the notion of covering maps. As a further example: Covering spaces are deeply interwined with the study of homotopy groups and, in particular, the fundamental group.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130252281
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- Sprache Englisch
- Größe H220mm x B150mm x T6mm
- Jahr 2009
- EAN 9786130252281
- Format Kartonierter Einband
- ISBN 978-613-0-25228-1
- Titel Covering Space
- Untertitel Mathematics, Algebraic topology, Continuous function, Surjective function, Topological space, Ordered pair, Homeomorphism, Homotopy, Riemannian geometry
- Gewicht 159g
- Herausgeber Alphascript Publishing
- Anzahl Seiten 96
- Genre Mathematik
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