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Topological Spaces: From Distance to Neighborhood

Topological Spaces: From Distance to Neighborhood
Catalogue Information
Field name Details
Dewey Class 514
Title Topological Spaces ([EBook]) : From Distance to Neighborhood / by Gerard Buskes, Arnoud van Rooij.
Author Buskes, Gerard
Added Personal Name Rooij, Arnoud C. M. van , 1936-
Other name(s) SpringerLink (Online service)
Publication New York, NY : Springer , 1997.
Physical Details XI, 313 pages : online resource.
Series Undergraduate texts in mathematics 0172-6056
ISBN 9781461206651
Summary Note This book is a text, not a reference, on Point-set Topology. It addresses itself to the student who is proficient in Calculus and has some experience with mathematical rigor, acquired, e.g., via a course in Advanced Calculus or Linear Algebra. To most beginners, Topology offers a double challenge. In addition to the strangeness of concepts and techniques presented by any new subject, there is an abrupt rise of the level of abstraction. It is a bad idea to teach a student two things at the same moment. To mitigate the culture shock, we move from the special to the general, dividing the book into three parts: 1. The Line and the Plane 2. Metric Spaces 3. Topological Spaces. In this way, the student has ample time to get acquainted with new ideas while still on familiar territory. Only after that, the transition to a more abstract point of view takes place. Elementary Topology preeminently is a subject with an extensive ar­ray of technical terms indicating properties of topological spaces. In the main body of the text, we have purposely restricted our mathematical vocabulary as much as is reasonably possible. Such an enterprise is risky. Doubtlessly, many readers will find us too thrifty. To meet them halfway, in Chapter 18 we briefly introduce and discuss a number of topological properties, but even there we do not touch on paracompactness, com­plete normality, and extremal disconnectedness-just to mention three terms that are not really esoteric.:
Contents note I The Line And The Plane -- 1 What Topology Is About -- 2 Axioms for ? -- 3 Convergent Sequences and Continuity -- 4 Curves in the Plane -- II Metric Spaces -- 5 Metrics -- 6 Open and Closed Sets -- 7 Completeness -- 8 Uniform Convergence -- 9 Sequential Compactness -- 10 Convergent Nets -- 11 Transition to Topology -- III Topological Spaces -- 12 Topological Spaces -- 13 Compactness and the Hausdorff Property -- 14 Products and Quotients -- 15 The Hahn-Tietze-Tong-Urysohn Theorems -- 16 Connectedness -- IV Postscript -- 18 A Smorgasbord for Further Study -- 19 Countable Sets -- Literature -- Index of Symbols -- Index of Terms.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-1-4612-0665-1
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