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Author Buskes, Gerard. author Topological Spaces [electronic resource] : From Distance to Neighborhood / by Gerard Buskes, Arnoud van Rooij New York, NY : Springer New York : Imprint: Springer, 1997 http://dx.doi.org/10.1007/978-1-4612-0665-1 XI, 313 p. online resource

SUMMARY

This book is a text, not a reference, on Point-set Thpology. 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. Th most beginners, Thpology 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. Th 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. Thpological 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 Thpology preeminently is a subject with an extensive arยญ ray 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. Th 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, comยญ plete normality, and extremal disconnectedness-just to mention three terms that are not really esoteric

CONTENT

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

Mathematics Topology Mathematics Topology

Location

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