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Overview"The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an ""explanation"" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are ""stable with respect to approximation"", and can be imposed on smooth functions via polynomial approximation." Full Product DetailsAuthor: Yosef Yomdin , Georges ComtePublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 2004 ed. Volume: 1834 Dimensions: Width: 15.50cm , Height: 1.00cm , Length: 23.50cm Weight: 0.640kg ISBN: 9783540206125ISBN 10: 3540206124 Pages: 190 Publication Date: 23 January 2004 Audience: General/trade , College/higher education , General , Tertiary & Higher Education Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |