Topology: An Introduction to the Point-Set and Algebraic Areas (Dover Books on Mathematics)

ch. 1. Logic, set theory, and the axiom of choice -- ch. 2. Metric spaces -- ch. 3. General topological spaces, bases, continuous functions, product spaces -- ch. 4. The special notions of compactness and connectedness -- ch. 5. Sequences, countability, separability, and metricization -- ch. 6. Quotients, local compactness, tietze extension, complete metrics, baire category -- ch. 7. Generalities about manifolds, the classification of surfaces -- ch. 8. The fundamental group -- ch. 9. Covering spaces -- ch. 10. Calculation of some fundamental groups, applications This accessible introduction to topology begins with a survey of basic topology, including the fundamentals of logic, set theory, and the axiom of choice. This is followed by discussions of metric spaces, general topological spaces, continuous functions, compactness and connectedness, and countability. The text addresses algebraic topology -- specifically 2-manifolds, covering spaces and fundamental groups. This book is designed as a textbook covering beginning topology for senior undergraduates and beginning graduate students Excellent text offers comprehensive coverage of elementary general topology as well as algebraic topology, specifically 2-manifolds, covering spaces and fundamental groups. The text is accessible to students at the advanced undergraduate or graduate level who are conversant with the basics of real analysis or advanced calculus. Problems, with selected solutions. Bibliography. 1975 edition.