Offering classroom-proven results, Differential Topology presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surface... read more
Lectures on Classical Differential Geometry: Second Edition by Dirk J. Struik Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, envelopes, more. Many problems and solutions. Bibliography.
General Topology by Stephen Willard Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.
Topology of 3-Manifolds and Related Topics by M.K. Fort, Jr., Daniel Silver Summaries and full reports from a 1961 conference discuss decompositions and subsets of 3-space; n-manifolds; knot theory; the Poincaré conjecture; and periodic maps and isotopies. Familiarity with algebraic topology required. 1962 edition.
Elements of Point-Set Topology by John D. Baum Basic treatment covers preliminaries (sets, relations, etc.), topological spaces, continuous functions (mappings) and homeomorphisms, special types of topological spaces, metric spaces, more. Geometric and axiomatic approach for easier accessibility. Exercises. Bibliography.
Introduction to Differentiable Manifolds by Louis Auslander, Robert E. MacKenzie This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.
Differential Manifolds by Antoni A. Kosinski Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.
Differential Topology: First Steps by Andrew H. Wallace Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. 1968 edition.
Introduction to Topology: Third Edition by Bert Mendelson Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.
Offering classroom-proven results, Differential Topology presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surfaces. This self-contained treatment features 88 helpful illustrations. Its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curves, surgery, classification of orientable surfaces, and Whitney's embedding theorem. Suitable for advanced undergraduate courses in introductory or differential topology, this volume also serves as a supplementary text in advanced calculus and physics courses, as well as a key source of information for students of mechanics.
Slightly corrected republication of the edition published by Marcel Dekker, Inc., New York, 1982.
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