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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Geometric Topology in Dimensions 2 and 3
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Geometric Topology in Dimensions 2 and 3
E.E. Moise (Broschiert, Englisch)
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Beschreibung
Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere… in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter. 90,94 €
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Technische Daten
Erscheinungsdatum
11.06.2013
Sprache
Englisch
EAN
9781461299080
Herausgeber
Springer US
Serien- oder Bandtitel
Graduate Texts in Mathematics
Sonderedition
Nein
Autor
E.E. Moise
Seitenanzahl
262
Einbandart
Broschiert
Schlagwörter
Cantor, Homeomorphism, Manifold, Morphism, Topology, theorem
Thema-Inhalt
PBP - Topologie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Humana, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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