Stock photo
Stock photo
Progress in Mathematics Ser.: Geometry of Subanalytic and Semialgebraic Sets by Masahiro Shiota (2012, Trade Paperback)
ThriftBooks (3880888)
99% positive feedback
Price:
US $75.23
ApproximatelyPHP 4,201.52
+ $15.53 shipping
Returns:
No returns, but backed by .
Condition:
Oops! Looks like we're having trouble connecting to our server.
Refresh your browser window to try again.
About this product
Product Identifiers
PublisherBirkhäuser Boston
ISBN-101461273781
ISBN-139781461273783
eBay Product ID (ePID)159987570
Product Key Features
Number of PagesXii, 434 Pages
LanguageEnglish
Publication NameGeometry of Subanalytic and Semialgebraic Sets
SubjectTopology, Set Theory, Logic, Geometry / Algebraic
Publication Year2012
TypeTextbook
AuthorMasahiro Shiota
Subject AreaMathematics
SeriesProgress in Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Height0.4 in
Item Weight24.3 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
Reviews"The main interest of the book is that it contains very deep results, some of which are new even for subanalytic or semialgebraic sets... These results are very important and provide foundations for the development of a 'tame topology' and a 'tame singularity theory.' Shiota's book is indispensable to every mathematician interested in these topics." -Bulletin of the AMS, "The main interest of the book is that it contains very deep results, some of which are new even for subanalytic or semialgebraic sets... These results are very important and provide foundations for the development of a 'tame topology' and a 'tame singularity theory.' Shiota's book is indispensable to every mathematician interested in these topics."-Bulletin of the AMS
Dewey Edition21
Series Volume Number150
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal516.3
Table Of ContentI. 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.
SynopsisReal 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., 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.
LC Classification NumberQA611-614.97
Be the first to write a review
