Topology for Analysis (Dover Books on Mathematics)

Description

Appropriate for both students and professionals, this volume starts with the first principles of topology and advances to general analysis. Three levels of examples and problems, ordered and numbered by degree of difficulty, illustrate important concepts. A 40-page appendix, featuring tables of theorems and counter examples, provides a valuable reference. From explorations of topological space, convergence, and separation axioms, the text proceeds to considerations of sup and weak topologies, products and quotients, compactness and compactification, and complete semimetric space. The concluding chapters explore metrization, topological groups, and function spaces. Each subject area is supplemented with examples, problems, and exercises that progress to increasingly rigorous levels. All examples and problems are classified as essential, optional, and advanced. Review: very good book for a beginner analyst - very deep and dense book with a modern look at analysis. It's like Munkres' Topology and Big Rudin in one volume. I am not sure why is it so cheap? Dover rocks. Review: Excellent complement for General Topology - I discovered this book as a Cambridge Maths undergraduate when it first came out in the early 1970s and it really helped complement the recommended texts and lecture notes. It is full of well explained examples, graded exercises and clear exposition and proofs. An especially interesting feature is the set of 42 tables of theorems and counterexamples in the appendix, doubtless slightly out of date now but still invaluable to those who, in the words of the author, absolutely ~must~ know whether every locally compact, completely regular, separable space is sigma-compact. (Although, to be totally honest, I have still never managed to find the answer to that particular combination, I don't consider this justifies reducing the overall 5-star rating). If I had not still got my 1972 copy, I would definitely buy this Dover reprint, even if it is slightly more expensive now than the £6.30 I paid for the hardback original. Be warned though, this is topology for analysis, as it says on the tin. The intuitions are almost exclusively analytically motivated and those in search of discussions of doughnut geometry or notions (co)homological and/or homotopic will need to search elsewhere.