Taste of Topology
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Description: If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs: a necessary, but not always exciting exercise one has to go through before one can read great works of literature in the original language. The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set theoretic topology (and to a tiny little bit of algebraic topology). It is accessible to undergraduates from the second year on, but even beginning graduate students canbenefit from some parts. Great care has been devoted to the selection of examples that are not self-serving, but already accessible for students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In some points, the book treats its material differently than other texts on the subject: * Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem; * nets are used extensively, in particular for an intuitive proof of Tychonoff's theorem; * a short and elegant, but little known proof for the Stone-Weierstrass theorem is given.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $49.95
Copyright year: 2005
Publication date: 12/7/2007
Size: 6.00" wide x 9.00" long x 0.50" tall
|Sets and Functions|
|Definitions and Examples|
|Open and Closed Sets|
|Convergence and Continuity|
|Compactness for Metric Spaces|
|Topological Spaces-Definitions and Examples|
|Continuity and Convergence of Nets|
|Systems of Continuous Functions|
|Urysohn's Lemma and Applications|
|The Stone-Čech Compactification|
|The Stone-Weierstraï¿½ Theorems|
|Basic Algebraic Topology|
|Homotopy and the Fundamental Group|
|The Classical Mittag-Leffler Theorem Derived from Bourbaki's|
|Failure of the Heine-Borel Theorem in Infinite-Dimensional Spaces|
|The Arzelï¿½-Ascoli Theorem|