| 书目名称 | Geometry of Subanalytic and Semialgebraic Sets | | 编辑 | Masahiro Shiota | | 视频video | | | 丛书名称 | Progress in Mathematics | | 图书封面 |  | | 描述 | 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 f | | 出版日期 | Book 1997 | | 关键词 | Finite; algebra; analytic function; analytic geometry; class; form; function; geometry; information; pdc; proo | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-2008-4 | | isbn_softcover | 978-1-4612-7378-3 | | isbn_ebook | 978-1-4612-2008-4Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer Science+Business Media New York 1997 |
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发表于 2025-3-21 17:06:04
