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| Author | : Theodore W. Gamelin |
| Publisher | : Courier Corporation |
| Total Pages | : 258 |
| Release | : 2013-04-22 |
| Genre | : Mathematics |
| ISBN | : 0486320189 |
This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
| Author | : Michael Henle |
| Publisher | : Courier Corporation |
| Total Pages | : 340 |
| Release | : 1994-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780486679662 |
Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
| Author | : Tej Bahadur Singh |
| Publisher | : Springer |
| Total Pages | : 452 |
| Release | : 2019-05-17 |
| Genre | : Mathematics |
| ISBN | : 9811369542 |
Topology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for studying problems in geometry and numerous other areas of mathematics. This book presents the basic concepts of topology, including virtually all of the traditional topics in point-set topology, as well as elementary topics in algebraic topology such as fundamental groups and covering spaces. It also discusses topological groups and transformation groups. When combined with a working knowledge of analysis and algebra, this book offers a valuable resource for advanced undergraduate and beginning graduate students of mathematics specializing in algebraic topology and harmonic analysis.
| Author | : Bert Mendelson |
| Publisher | : Courier Corporation |
| Total Pages | : 226 |
| Release | : 2012-04-26 |
| Genre | : Mathematics |
| ISBN | : 0486135098 |
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.
| Author | : Saul Stahl |
| Publisher | : John Wiley & Sons |
| Total Pages | : 430 |
| Release | : 2014-08-21 |
| Genre | : Mathematics |
| ISBN | : 1118546148 |
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” —CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition: • Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being • Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods • Bridges seemingly disparate topics by creating thoughtful and logical connections • Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.
| Author | : Robert A Conover |
| Publisher | : Courier Corporation |
| Total Pages | : 276 |
| Release | : 2014-05-21 |
| Genre | : Mathematics |
| ISBN | : 0486780015 |
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 topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com
| Author | : Min Yan |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 285 |
| Release | : 2016-02-22 |
| Genre | : Mathematics |
| ISBN | : 3110413027 |
The aim of the book is to give a broad introduction of topology to undergraduate students. It covers the most important and useful parts of the point-set as well as the combinatorial topology. The development of the material is from simple to complex, concrete to abstract, and appeals to the intuition of readers. Attention is also paid to how topology is actually used in the other fields of mathematics. Over 150 illustrations, 160 examples and 600 exercises will help readers to practice and fully understand the subject. Contents: Set and Map Metric Space Graph Topology Topological Concepts Complex Topological Properties Surface Topics in Point Set Topology Index
| Author | : V. A. Vasilʹev |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 165 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821821628 |
This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, homology and cohomology, intersection index, etc. The author notes, "The lecture note origins of the book left a significant imprint on itsstyle. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs." He concludes, "As a rule, only those proofs (or sketches of proofs) that are interesting per se and have importantgeneralizations are presented."
| Author | : Andrew H. Wallace |
| Publisher | : Courier Corporation |
| Total Pages | : 212 |
| Release | : 2007-02-27 |
| Genre | : Mathematics |
| ISBN | : 0486457869 |
Originally published: Homology theory on algebraic varieties. New York: Pergamon Press, 1957.
| Author | : Crump W. Baker |
| Publisher | : |
| Total Pages | : 155 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9781575240084 |
The fundamental concepts of general topology are covered in this text whic can be used by students with only an elementary background in calculus. Chapters cover: sets; functions; topological spaces; subspaces; and homeomorphisms.
