Geometry of Subanalytic and Semialgebraic Sets
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 re...
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| Format: | eBook |
| Language: | English |
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Boston, MA
Birkhäuser
1997, 1997
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| Edition: | 1st ed. 1997 |
| Series: | Progress in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of 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