Geometry of subanalytic and semialgebraic sets:
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 fundamen...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1997
|
| Series: | Progress in mathematics
150 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| 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. |
| Physical Description: | XII, 431 S. |
| ISBN: | 0817640002 3764340002 |
Staff View
MARC
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| 245 | 1 | 0 | |a Geometry of subanalytic and semialgebraic sets |c Masahiro Shiota |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1997 | |
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| 490 | 1 | |a Progress in mathematics |v 150 | |
| 520 | 3 | |a 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. | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Introduction
.....................................................
vii
CHAPTER I. PRELIMINARIES
..................................1
§1.1.
Whitney stratifications
.....................................1
§1.2.
Subanalytic sets and semialgebraic sets
......................40
§1.3.
PL topology and C°°
triangulations
.........................54
CHAPTER II. X-SETS
........................................ 95
§11.1.
X-sets
...................................................97
§11.2.
Triangulations
of X-sets
..................................116
§11.3.
Triangulations
of X-functions
.............................. 131
§11.4.
Triangulations
of semialgebraic and Xo sets and functions
.....146
§11.5.
Cr X-manifolds
..........................................156
§11.6.
Х
-triviality
of X-maps
....................................186
§11.7.
X-singularity theory
.........................,.........,., 235
CHAPTER III. HAUPTVERMUTUNC FOR POLYHEDRA
,,.,,,, 2,7
С
§111.1.
Certain conditions for two poly
hedra
to be PL homeomorphic
, 270
§111.2.
Proofs of Theorems III.l.l and III.
1.2 .........,,..,.,,...., 274
CHAPTER IV.
TRIANGULATIONS
OF X-MAPS
...............305
§IV.l. Conditions for
Х
-maps to be triangulable
...................305
§IV.2. Proofs of Theorems IV.
1.1,
IV.1.2, IV.
1.2
and IV.
1.2 ........ 314
§IV.3. Local and global
Х
-triangulations
and uniqueness
............ 359
§IV.4. Proofs of Theorems IV.
1.10,
IV.
1.13
and IV.
1.13 ............369
CHAPTER V. 2J-SETS
....................................... 388
§V.l. Case where any 3)-set is locally
semilinear .................. 389
§V.2. Case where there exists a 2)-set which is not locally
semilinear. 405
Bibliography
.................................................. 421
List of Notation
............................................... 425
Index
.........................................................427
|
| any_adam_object | 1 |
| author | Shiota, Masahiro |
| author_facet | Shiota, Masahiro |
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| dewey-full | 516.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3 |
| dewey-search | 516.3 |
| dewey-sort | 3516.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011612490 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:12:44Z |
| institution | BVB |
| isbn | 0817640002 3764340002 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007822259 |
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| physical | XII, 431 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Shiota, Masahiro Verfasser aut Geometry of subanalytic and semialgebraic sets Masahiro Shiota Boston [u.a.] Birkhäuser 1997 XII, 431 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 150 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. Ensemble semi-algébrique Jussieu Ensemble sous-analytique Jussieu Ensembles semi-algébriques ram Ensembles semi-analytiques ram Stratification Whitney Jussieu Semialgebraic sets Semianalytic sets Algebraische Menge (DE-588)4141840-2 gnd rswk-swf Subanalytische Menge (DE-588)4238162-9 gnd rswk-swf Subanalytische Menge (DE-588)4238162-9 s DE-604 Algebraische Menge (DE-588)4141840-2 s Progress in mathematics 150 (DE-604)BV000004120 150 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007822259&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shiota, Masahiro Geometry of subanalytic and semialgebraic sets Progress in mathematics Ensemble semi-algébrique Jussieu Ensemble sous-analytique Jussieu Ensembles semi-algébriques ram Ensembles semi-analytiques ram Stratification Whitney Jussieu Semialgebraic sets Semianalytic sets Algebraische Menge (DE-588)4141840-2 gnd Subanalytische Menge (DE-588)4238162-9 gnd |
| subject_GND | (DE-588)4141840-2 (DE-588)4238162-9 |
| title | Geometry of subanalytic and semialgebraic sets |
| title_auth | Geometry of subanalytic and semialgebraic sets |
| title_exact_search | Geometry of subanalytic and semialgebraic sets |
| title_full | Geometry of subanalytic and semialgebraic sets Masahiro Shiota |
| title_fullStr | Geometry of subanalytic and semialgebraic sets Masahiro Shiota |
| title_full_unstemmed | Geometry of subanalytic and semialgebraic sets Masahiro Shiota |
| title_short | Geometry of subanalytic and semialgebraic sets |
| title_sort | geometry of subanalytic and semialgebraic sets |
| topic | Ensemble semi-algébrique Jussieu Ensemble sous-analytique Jussieu Ensembles semi-algébriques ram Ensembles semi-analytiques ram Stratification Whitney Jussieu Semialgebraic sets Semianalytic sets Algebraische Menge (DE-588)4141840-2 gnd Subanalytische Menge (DE-588)4238162-9 gnd |
| topic_facet | Ensemble semi-algébrique Ensemble sous-analytique Ensembles semi-algébriques Ensembles semi-analytiques Stratification Whitney Semialgebraic sets Semianalytic sets Algebraische Menge Subanalytische Menge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007822259&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT shiotamasahiro geometryofsubanalyticandsemialgebraicsets |