A Taste of Topology

Having evolved from Runde's notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology. In places, Runde's text treats its material differently to other books on the subject, providing a fresh perspective.

This should be a revelation for mathematics undergraduates. Having evolved from Runde's notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The well-chosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Runde's text treats its material differently to other books on the subject, providing a fresh perspective. For example, 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; and a short and elegant, but little known proof for the Stone-Weierstrass theorem is given.

Covers all relevant topics in introductory topology - grew out of course notes from an introductory topology course Unique in its scope and approach on various points - for example, it provides coverage of some influential areas often overlooked by other textbooks, like usage of nets and the Stone-Cech compactification Carefully selected examples and exercises are provided throughout to illustrate key concepts Includes supplementary material: sn.pub/extras

Contenu

Preface.- Introduction.- Set Theory.- Metric Spaces.- Set Theoretic Topology.- Systems of Continuous Functions.- Basic Algebraic Topology.- The Classical Mittag-Leffler Theorem Derived from Bourbaki's.- Failure of the Heine-Borel Theorem in Infinite-Dimensional Spaces.- The Arzela-Ascoli Theorem.- References.- List of Symbols.- Index.