Introduction to Topology

The formation of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics represent one of the most important developments in 20th-century mathematics. This text takes a unique introductory approach to the subject, leadin [...]
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The formation of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics represent one of the most important developments in 20th-century mathematics. This text takes a unique introductory approach to the subject, leading students through a number of nontrivial applications of metric space topology to analysis, so that the relevance of topology to analysis is clearly established. In addition, the treatment of topics from elementary algebraic topology concentrates on results with concrete geometric meaning with relatively little algebraic formalism, while providing proofs of some highly nontrivial results. The first two chapters examine metric space and point-set topology; the remaining two chapters explore algebraic topological material. Carefully chosen exercises are integrated into the text, and a list of notations and bibliographical references are provided. Solutions to selected exercises have been added to this edition.