Geometry of Subanalytic and Semialgebraic Sets:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1997
|
| Schriftenreihe: | Progress in Mathematics
150 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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 development 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 differences 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 analytic 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 |
| Beschreibung: | 1 Online-Ressource (XII, 434 p) |
| ISBN: | 9781461220084 9781461273783 |
| DOI: | 10.1007/978-1-4612-2008-4 |
Internformat
MARC
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| 490 | 1 | |a Progress in Mathematics |v 150 | |
| 500 | |a 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 development 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 differences 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 analytic 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 | ||
| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
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| author | Shiota, Masahiro 1947- |
| author_GND | (DE-588)172372992 |
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| author_sort | Shiota, Masahiro 1947- |
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| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-2008-4 |
| format | Electronic eBook |
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| id | DE-604.BV042419955 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461220084 9781461273783 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855372 |
| oclc_num | 879624697 |
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| physical | 1 Online-Ressource (XII, 434 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser Boston |
| record_format | marc |
| series | Progress in Mathematics |
| series2 | Progress in Mathematics |
| spelling | Shiota, Masahiro 1947- Verfasser (DE-588)172372992 aut Geometry of Subanalytic and Semialgebraic Sets by Masahiro Shiota Boston, MA Birkhäuser Boston 1997 1 Online-Ressource (XII, 434 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 150 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 development 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 differences 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 analytic 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 Mathematics Geometry, algebraic Geometry Logic, Symbolic and mathematical Topology Algebraic topology Algebraic Geometry Algebraic Topology Mathematical Logic and Foundations Mathematik Subanalytische Menge (DE-588)4238162-9 gnd rswk-swf Algebraische Menge (DE-588)4141840-2 gnd rswk-swf Subanalytische Menge (DE-588)4238162-9 s 1\p DE-604 Algebraische Menge (DE-588)4141840-2 s 2\p DE-604 Progress in Mathematics 150 (DE-604)BV000004120 150 https://doi.org/10.1007/978-1-4612-2008-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Shiota, Masahiro 1947- Geometry of Subanalytic and Semialgebraic Sets Progress in Mathematics Mathematics Geometry, algebraic Geometry Logic, Symbolic and mathematical Topology Algebraic topology Algebraic Geometry Algebraic Topology Mathematical Logic and Foundations Mathematik Subanalytische Menge (DE-588)4238162-9 gnd Algebraische Menge (DE-588)4141840-2 gnd |
| subject_GND | (DE-588)4238162-9 (DE-588)4141840-2 |
| 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 by Masahiro Shiota |
| title_fullStr | Geometry of Subanalytic and Semialgebraic Sets by Masahiro Shiota |
| title_full_unstemmed | Geometry of Subanalytic and Semialgebraic Sets by Masahiro Shiota |
| title_short | Geometry of Subanalytic and Semialgebraic Sets |
| title_sort | geometry of subanalytic and semialgebraic sets |
| topic | Mathematics Geometry, algebraic Geometry Logic, Symbolic and mathematical Topology Algebraic topology Algebraic Geometry Algebraic Topology Mathematical Logic and Foundations Mathematik Subanalytische Menge (DE-588)4238162-9 gnd Algebraische Menge (DE-588)4141840-2 gnd |
| topic_facet | Mathematics Geometry, algebraic Geometry Logic, Symbolic and mathematical Topology Algebraic topology Algebraic Geometry Algebraic Topology Mathematical Logic and Foundations Mathematik Subanalytische Menge Algebraische Menge |
| url | https://doi.org/10.1007/978-1-4612-2008-4 |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT shiotamasahiro geometryofsubanalyticandsemialgebraicsets |