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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."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.
Synopsis:This stimulating introduction employs the language of point set topology to define and discuss topological groups. It examines settheoretic topology and its applications in function spaces as well as homotopy and the fundamental group. Wellchosen exercises and problems serve as reinforcements. 1967 edition. Includes 99 illustrations.
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
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Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry


