The Resource Geometry of Subanalytic and Semialgebraic Sets, by Masahiro Shiota, (electronic resource)

Geometry of Subanalytic and Semialgebraic Sets, by Masahiro Shiota, (electronic resource)

Label
Geometry of Subanalytic and Semialgebraic Sets
Title
Geometry of Subanalytic and Semialgebraic Sets
Statement of responsibility
by Masahiro Shiota
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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
Member of
http://library.link/vocab/creatorName
Shiota, Masahiro
Dewey number
514
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
f8hyGBFpJd4
Image bit depth
0
Language note
English
LC call number
QA611-614.97
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Progress in Mathematics,
Series volume
150
http://library.link/vocab/subjectName
  • Topology
  • Geometry, algebraic
  • Algebraic topology
  • Logic, Symbolic and mathematical
  • Geometry
  • Topology
  • Algebraic Geometry
  • Algebraic Topology
  • Mathematical Logic and Foundations
  • Geometry
Label
Geometry of Subanalytic and Semialgebraic Sets, by Masahiro Shiota, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
I. Preliminaries -- §1.1. Whitney stratifications -- §1.2. Subanalytic sets and semialgebraic sets -- §1.3. PL topology and C? triangulations -- II. X-Sets -- §11.1. X-sets -- §11.2. Triangulations of X-sets -- §11.3. Triangulations of X functions -- §11.4. Triangulations of semialgebraic and X0 sets and functions -- §11.5. Cr X-manifolds -- §11.6. X-triviality of X-maps -- §11.7. X-singularity theory -- III. Hauptvermutung For Polyhedra -- §III.1. Certain conditions for two polyhedra to be PL homeomorphic -- §III.2. Proofs of Theorems III.1.1 and III.1.2 -- IV. Triangulations of X-Maps -- §IV.l. Conditions for X-maps to be triangulable -- §IV.2. Proofs of Theorems IV.1.1, IV.1.2, IV.1.2? and IV.1.2? -- §IV.3. Local and global X-triangulations and uniqueness -- §IV.4. Proofs of Theorems IV.1.10, IV.1.13 and IV.1.13? -- V. D-Sets -- §V.1. Case where any D-set is locally semilinear -- §V.2. Case where there exists a D-set which is not locally semilinear -- List of Notation
Dimensions
unknown
Edition
First edition.
Extent
1 online resource (XII, 434 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461220084
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-2008-4
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089797
  • (SSID)ssj0001296929
  • (PQKBManifestationID)11886709
  • (PQKBTitleCode)TC0001296929
  • (PQKBWorkID)11353920
  • (PQKB)10928391
  • (DE-He213)978-1-4612-2008-4
  • (MiAaPQ)EBC3076328
  • (EXLCZ)993400000000089797
Label
Geometry of Subanalytic and Semialgebraic Sets, by Masahiro Shiota, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
I. Preliminaries -- §1.1. Whitney stratifications -- §1.2. Subanalytic sets and semialgebraic sets -- §1.3. PL topology and C? triangulations -- II. X-Sets -- §11.1. X-sets -- §11.2. Triangulations of X-sets -- §11.3. Triangulations of X functions -- §11.4. Triangulations of semialgebraic and X0 sets and functions -- §11.5. Cr X-manifolds -- §11.6. X-triviality of X-maps -- §11.7. X-singularity theory -- III. Hauptvermutung For Polyhedra -- §III.1. Certain conditions for two polyhedra to be PL homeomorphic -- §III.2. Proofs of Theorems III.1.1 and III.1.2 -- IV. Triangulations of X-Maps -- §IV.l. Conditions for X-maps to be triangulable -- §IV.2. Proofs of Theorems IV.1.1, IV.1.2, IV.1.2? and IV.1.2? -- §IV.3. Local and global X-triangulations and uniqueness -- §IV.4. Proofs of Theorems IV.1.10, IV.1.13 and IV.1.13? -- V. D-Sets -- §V.1. Case where any D-set is locally semilinear -- §V.2. Case where there exists a D-set which is not locally semilinear -- List of Notation
Dimensions
unknown
Edition
First edition.
Extent
1 online resource (XII, 434 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461220084
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-2008-4
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089797
  • (SSID)ssj0001296929
  • (PQKBManifestationID)11886709
  • (PQKBTitleCode)TC0001296929
  • (PQKBWorkID)11353920
  • (PQKB)10928391
  • (DE-He213)978-1-4612-2008-4
  • (MiAaPQ)EBC3076328
  • (EXLCZ)993400000000089797

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