This 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.
Product Identifiers
Publisher
Springer-Verlag New York Inc.
ISBN-13
9781441928238
eBay Product ID (ePID)
178211038
Product Key Features
Author
J. Dixmier
Publication Name
General Topology
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
2010
Type
Textbook
Number of Pages
141 Pages
Dimensions
Item Height
235mm
Item Width
155mm
Item Weight
500g
Additional Product Features
Title_Author
J. Dixmier
Series Title
Undergraduate Texts in Mathematics
Country/Region of Manufacture
United States
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