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Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: "continuous topology," represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and "geometric topology," covered by nine sections on connectivity properties, topological...
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Engaging introduction to that curious feature of mathematics which provides framework for so many structures in biology, chemistry, and the arts. Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more.
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Mathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers. The precise exposition of the...
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Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds. No previous knowledge of topology is necessary for this text, which offers introductory material regarding open and closed sets and continuous...
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Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract, the treatment emphasizes the geometric nature of the...
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Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set...
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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...
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Español
Description
En este estudio, se examina la subestructura matemática de las obras del artista gráfico neerlandés M.C. Escher. Los efectos matemáticos en las obras de Escher pueden clasificarse en ciertos temas. Los más importantes pueden ordenarse como la división regular del plano, las paradojas visuales y las ficciones sobre la estructura de la perspectiva y la topología geométrica. Para cada uno de estos temas, se puede decir que Escher está influenciado...
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Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary...
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Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Includes problems and exercises, correlated with examples. Bibliography. 1978 edition.
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Alexandroff's beautiful and elegant introduction to topology was originally published in 1932 as an extension of certain aspects of Hilbert's Anschauliche Geometrie. The text has long been recognized as one of the finest presentations of the fundamental concepts, vital for mathematicians who haven't time for extensive study and for beginning investigators. The book is not a substitute for a systematic text, but an unusually useful intuitive approach...
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This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems. Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation...
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A fresh approach to introductory topology, this volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. The first two chapters consider metric space and point-set topology; the second two, algebraic topological material. 1983 edition. Solutions to Selected Exercises. List of Notations....
15) General Topology
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"The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure," noted the Bulletin of the American Mathematical Society upon the 1955 publication of John L. Kelley's General Topology. This comprehensive treatment for beginning graduate-level students immediately found a significant audience, and it remains a highly worthwhile and relevant book for students of topology and for professionals in many areas....
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Classroom-tested and much-cited, this concise text offers a valuable and instructive introduction for undergraduates to the basic concepts of topology. It takes an intuitive rather than an axiomatic viewpoint, and can serve as a supplement as well as a primary text. A few selected topics allow students to acquire a feeling for the types of results and the methods of proof in mathematics, including mathematical induction. Subsequent problems deal with...
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This text for upper-level undergraduates and graduate students focuses on key notions and results in functional analysis. Extending beyond the boundaries of Hilbert and Banach space theory, it explores aspects of analysis relevant to the solution of partial differential equations. The three-part treatment begins with topological vector spaces and spaces of functions, progressing to duality and spaces of distribution, and concluding with tensor products...
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English
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Designed for a one-year course in topological vector spaces, this text is geared toward advanced undergraduates and beginning graduate students of mathematics. The subjects involve properties employed by researchers in classical analysis, differential and integral equations, distributions, summability, and classical Banach and Frechét spaces. Optional problems with hints and references introduce non-locally convex spaces, Köthe-Toeplitz spaces,...
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An elementary text that can be understood by anyone with a background in high school geometry, Invitation to Combinatorial Topology offers a stimulating initiation to important topological ideas. This translation from the original French does full justice to the text's coherent presentation as well as to its rich historical content. Subjects include the problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, and topological...
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Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the...
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