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OverviewThis book is a course in general topology, intended for students in the first year of the second cycle (in other words, students in their third univer sity year). The course was taught during the first semester of the 1979-80 academic year (three hours a week of lecture, four hours a week of guided work). Topology is the study of the notions of limit and continuity and thus is, in principle, very ancient. However, we shall limit ourselves to the origins of the theory since the nineteenth century. One of the sources of topology is the effort to clarify the theory of real-valued functions of a real variable: uniform continuity, uniform convergence, equicontinuity, Bolzano-Weierstrass theorem (this work is historically inseparable from the attempts to define with precision what the real numbers are). Cauchy was one of the pioneers in this direction, but the errors that slip into his work prove how hard it was to isolate the right concepts. Cantor came along a bit later; his researches into trigonometric series led him to study in detail sets of points of R (whence the concepts of open set and closed set in R, which in his work are intermingled with much subtler concepts). The foregoing alone does not justify the very general framework in which this course is set. The fact is that the concepts mentioned above have shown themselves to be useful for objects other than the real numbers. Full Product DetailsAuthor: J. Dixmier , S. K. BerberianPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 1984 Dimensions: Width: 15.50cm , Height: 0.80cm , Length: 23.50cm Weight: 0.500kg ISBN: 9781441928238ISBN 10: 1441928235 Pages: 141 Publication Date: 03 December 2010 Audience: Professional and scholarly , Professional and scholarly , Professional & Vocational , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: Out of print, replaced by POD  We will order this item for you from a manufatured on demand supplier. Table of ContentsI Topological Spaces.- II Limits. Continuity.- III Constructions of Topological Spaces.- IV Compact Spaces.- V Metric Spaces.- VI Limits of Functions.- VII Numerical Functions.- VIII Normed Spaces.- IX Infinite Sums.- X Connected Spaces.- Exercises.- Index of Notations.- Index of Terminology.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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