The Resource Geometry of subanalytic and semialgebraic sets, Masahiro Shiota, (electronic resource)

Geometry of subanalytic and semialgebraic sets, Masahiro Shiota, (electronic resource)

Label
Geometry of subanalytic and semialgebraic sets
Title
Geometry of subanalytic and semialgebraic sets
Statement of responsibility
Masahiro Shiota
Creator
Subject
Genre
Language
eng
Summary
Subanalytic and semialgebraic sets were introduced for topological and systematic investigations of real analytic and algebraic sets. One of the author's purposes is to show that almost all (known and unknown) properties of subanalytic and semialgebraic sets follow abstractly from some fundamental axioms. Another is to develop methods of proof that use finite processes instead of integration of vector fields. The proofs are elementary, but the results obtained are new and significant - for example, for singularity theorists and topologists. Further, the new methods and tools developed provide solid foundations for further research by model theorists (logicians) who are interested in applications of model theory to geometry. A knowledge of basic topology is required
Member of
Action
digitized
Cataloging source
OCLCE
http://library.link/vocab/creatorDate
1947-
http://library.link/vocab/creatorName
Shiota, Masahiro
Dewey number
516.3
Index
index present
LC call number
QA564
LC item number
.S46 1997eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Progress in mathematics
Series volume
v. 150
http://library.link/vocab/subjectName
  • Semialgebraic sets
  • Semianalytic sets
  • Ensemble sous-analytique
  • Ensemble semi-algébrique
  • Stratification Whitney
  • Ensembles semi-analytiques
  • Ensembles semi-algébriques
  • Semialgebraische Menge
  • Subanalytische Menge
  • Semialgebraic sets
  • Semianalytic sets
Label
Geometry of subanalytic and semialgebraic sets, Masahiro Shiota, (electronic resource)
Link
http://dx.doi.org/10.1007/978-1-4612-2008-4
Instantiates
Publication
Antecedent source
file reproduced from original
Bibliography note
Includes bibliographical references (pages 421-424) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
black and white
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
I. Preliminaries -- ʹ1.1. Whitney stratifications -- ʹ1.2. Subanalytic sets and semialgebraic sets -- ʹ1.3. PL topology and C? triangulations -- II. X-Sets -- ʹ11.1. X-sets -- ʹ11.2. Triangulations of X-sets -- ʹ11.3. Triangulations of X functions -- ʹ11.4. Triangulations of semialgebraic and X0 sets and functions -- ʹ11.5. Cr X-manifolds -- ʹ11.6. X-triviality of X-maps -- ʹ11.7. X-singularity theory -- III. Hauptvermutung For Polyhedra -- ʹIII.1. Certain conditions for two polyhedra to be PL homeomorphic -- ʹIII.2. Proofs of Theorems III.1.1 and III.1.2 -- IV. Triangulations of X-Maps -- ʹIV.l. Conditions for X-maps to be triangulable -- ʹIV.2. Proofs of Theorems IV.1.1, IV.1.2, IV.1.2? and IV.1.2? -- ʹIV.3. Local and global X-triangulations and uniqueness -- ʹIV.4. Proofs of Theorems IV.1.10, IV.1.13 and IV.1.13? -- V. D-Sets -- ʹV.1. Case where any D-set is locally semilinear -- ʹV.2. Case where there exists a D-set which is not locally semilinear -- List of Notation
Dimensions
unknown
Extent
1 online resource (xii, 431 pages).
Form of item
online
Isbn
9781461220084
Isbn Type
(electronic bk.)
Level of compression
  • lossless
  • lossy
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-4612-2008-4
Reformatting quality
  • preservation
  • access
Reproduction note
Electronic reproduction.
Specific material designation
remote
System control number
  • (OCoLC)812612981
  • (OCoLC)ocn812612981
System details
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Label
Geometry of subanalytic and semialgebraic sets, Masahiro Shiota, (electronic resource)
Link
http://dx.doi.org/10.1007/978-1-4612-2008-4
Publication
Antecedent source
file reproduced from original
Bibliography note
Includes bibliographical references (pages 421-424) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
black and white
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
I. Preliminaries -- ʹ1.1. Whitney stratifications -- ʹ1.2. Subanalytic sets and semialgebraic sets -- ʹ1.3. PL topology and C? triangulations -- II. X-Sets -- ʹ11.1. X-sets -- ʹ11.2. Triangulations of X-sets -- ʹ11.3. Triangulations of X functions -- ʹ11.4. Triangulations of semialgebraic and X0 sets and functions -- ʹ11.5. Cr X-manifolds -- ʹ11.6. X-triviality of X-maps -- ʹ11.7. X-singularity theory -- III. Hauptvermutung For Polyhedra -- ʹIII.1. Certain conditions for two polyhedra to be PL homeomorphic -- ʹIII.2. Proofs of Theorems III.1.1 and III.1.2 -- IV. Triangulations of X-Maps -- ʹIV.l. Conditions for X-maps to be triangulable -- ʹIV.2. Proofs of Theorems IV.1.1, IV.1.2, IV.1.2? and IV.1.2? -- ʹIV.3. Local and global X-triangulations and uniqueness -- ʹIV.4. Proofs of Theorems IV.1.10, IV.1.13 and IV.1.13? -- V. D-Sets -- ʹV.1. Case where any D-set is locally semilinear -- ʹV.2. Case where there exists a D-set which is not locally semilinear -- List of Notation
Dimensions
unknown
Extent
1 online resource (xii, 431 pages).
Form of item
online
Isbn
9781461220084
Isbn Type
(electronic bk.)
Level of compression
  • lossless
  • lossy
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-4612-2008-4
Reformatting quality
  • preservation
  • access
Reproduction note
Electronic reproduction.
Specific material designation
remote
System control number
  • (OCoLC)812612981
  • (OCoLC)ocn812612981
System details
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

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