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Other titles in the Dover Phoenix Editions series:
Topology: An Introduction with Application to Topological Groups (Phoenix Edition)by George Mccarty
Synopses & Reviews
"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 set-theoretic 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. Well-chosen 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.
Topology, sometimes described as "rubber-sheet geometry", is crucial to modern mathematics and to many other disciplines--from 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.
This stimulating introduction employs the language of point set topology to define and discuss topological groups. It examines set-theoretic topology and its applications in function spaces as well as homotopy and the fundamental group. Well-chosen exercises and problems serve as reinforcements. 1967 edition. Includes 99 illustrations.
Table of Contents
1. Sets and Functions
3. Metric Spaces
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
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