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Topology: An Introduction with Application to Topological Groups (Phoenix Edition)
Synopses & ReviewsPublisher Comments:"Admirably meets the topology requirements for the pregraduate training of research mathematicians."and#8212;American Mathematical Monthly Topology, sometimes described as "rubbersheet geometry," is crucial to modern mathematics and to many other disciplinesand#8212;from quantum mechanics to sociology. This stimulating introduction to the field will give the student a familiarity with elementary point set topology, including an easy acquaintance with the line and the plane, knowledge often useful in graduate mathematics programs. The book is not a collection of topics, rather it early employs the language of point set topology to define and discuss topological groups. These geometric objects in turn motivate a further discussion of settheoretic topology and of its applications in function spaces. An introduction to homotopy and the fundamental group then brings the student's new theoretical knowledge to bear on very concrete problems: the calculation of the fundamental group of the circle and a proof of the fundamental theorem of algebra. Finally, the abstract development is brought to satisfying fruition with the classification of topological groups by equivalence under local isomorphism. Throughout the book there is a sustained geometric development and#8212; a single thread of reasoning which unifies the topological course. One of the special features of this work is its wellchosen exercises, along with a selection of problems in each chapter that contain interesting applications and further theory. Careful study of the text and diligent performance of the exercises will enable the student to achieve an excellent working knowledge of topology and a useful understanding of its applications. Moreover, the author's unique teaching approach lends an extra dimension of effectiveness to the books: "Of particular interest is the remarkable pedagogy evident in this work. The author converses with the reader on a personal basis. He speaks with him, questions him, challenges him, andand#8212;best of alland#8212;occasionally leaves him to his own devices."and#8212;American Scientist Synopsis:"Admirably meets the topology requirements for the pregraduate training of research mathematicians."American Mathematical Monthly Crucial to modern mathematics, topology is equally essential to many other disciplines, from quantum mechanics to sociology. This stimulating introduction employs the language of point set topology to define and discuss topological groups. The text examines settheoretic topology and its applications in function spaces, as well as homotopy and the fundamental group. This new theoretical knowledge is applied to concrete problems, such as the calculation of the fundamental group of the circle and a proof of the fundamental theorem of algebra. The abstract development concludes with the classification of topological groups by equivalence under local isomorphism. Throughout this text, a sustained geometric development functions as a single thread of reasoning that unifies the topological course. Wellchosen exercises, along with a selection of problems in each chapter that contain interesting applications and further theory, help solidify students' working knowledge of topology and its applications. Synopsis:Topology, sometimes described as "rubbersheet geometry", is crucial to modern mathematics and to many other disciplinesfrom quantum mechanics to sociology. This stimulating introduction to the field gives students a familiarity with the elementary point set of topology, including an easy acquaintance with the line and the plane, knowledge often useful in graduate mathematics programs.
Table of ContentsIntroduction
1. Sets and Functions 2. Groups 3. Metric Spaces 4. Topologies 5. Topological Groups 6. Compactness and Connectedness 7. Function Spaces 8. The Fundamental Group 9. The Fundamental Group of the Circle 10. Locally Isomorphic Groups Indexes What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
Related Subjects
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry


