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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Geometry of Subanalytic and Semialgebraic Sets
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Geometry of Subanalytic and Semialgebraic Sets
Masahiro Shiota (Broschiert, Englisch)
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Beschreibung
Real analytic sets in Euclidean space (Le. , sets defined locally at each point of Euclidean space by the vanishing of an analytic function) were first investigated in the 1950's by H. Cartan [Car], H. Whitney [WI-3], F. Bruhat [W-B] and others. Their approach was to derive information about real analytic sets from properties of their complexifications. After some basic geometrical and topological… facts were established, however, the study of real analytic sets stagnated. This contrasted the rapid develop ment of complex analytic geometry which followed the groundbreaking work of the early 1950's. Certain pathologies in the real case contributed to this failure to progress. For example, the closure of -or the connected components of-a constructible set (Le. , a locally finite union of differ ences of real analytic sets) need not be constructible (e. g. , R - {O} and 3 2 2 { (x, y, z) E R : x = zy2, x + y2 -=I- O}, respectively). Responding to this in the 1960's, R. Thorn [Thl], S. Lojasiewicz [LI,2] and others undertook the study of a larger class of sets, the semianalytic sets, which are the sets defined locally at each point of Euclidean space by a finite number of ana lytic function equalities and inequalities. They established that semianalytic sets admit Whitney stratifications and triangulations, and using these tools they clarified the local topological structure of these sets. For example, they showed that the closure and the connected components of a semianalytic set are semianalytic. 85,59 €
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Technische Daten
Erscheinungsdatum
13.10.2012
Sprache
Englisch
EAN
9781461273783
Herausgeber
Birkhäuser Boston
Serien- oder Bandtitel
Progress in Mathematics
Sonderedition
Nein
Autor
Masahiro Shiota
Seitenanzahl
434
Einbandart
Broschiert
Schlagwörter
Finite, algebra, analytic function, analytic geometry, class, form, function, geometry, information, pdc, proof, set, sets, tool, topology
Thema-Inhalt
PBP - Topologie
PBMW - Algebraische Geometrie
PBPD - Algebraische Topologie
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
PBM - Geometrie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Birkhäuser, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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