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Topology: An Introduction with Application to Topological Groups

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Topology: An Introduction with Application to Topological Groups Cover

 

Synopses & Reviews

Publisher Comments:

"Admirably meets the topology requirements for the pregraduate training of research mathematicians."—American Mathematical Monthly

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 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 set-theoretic 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 — a single thread of reasoning which unifies the topological course.

One of the special features of this work is its well-chosen 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, and—best of all—occasionally leaves him to his own devices."—American Scientist

Synopsis:

Covers sets and functions, groups, metric spaces, topologies, topological groups, compactness and connectedness, function spaces, the fundamental group, the fundamental group of the circle, locally isomorphic groups, more. 1967 edition.

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 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.

Synopsis:

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.

 

Product Details

ISBN:
9780486656335
Author:
McCarty, George
Publisher:
Dover Publications
Author:
McCarty, George
Author:
Mathematics
Location:
New York :
Subject:
Science
Subject:
Geology
Subject:
Algebra - Linear
Subject:
Topology
Subject:
Topological groups
Subject:
Earth Sciences - Geology
Subject:
General Mathematics
Subject:
Geology-General
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
38
Publication Date:
20110131
Binding:
TRADE PAPER
Language:
English
Illustrations:
99
Pages:
304
Dimensions:
8.5 x 5.63 in 0.64 lb

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Related Subjects


» Science and Mathematics » Geology » General
» Science and Mathematics » Mathematics » Advanced
» Science and Mathematics » Mathematics » General
» Science and Mathematics » Mathematics » Topology
» Science and Mathematics » Physics » General
» Young Adult » General

Topology: An Introduction with Application to Topological Groups Used Trade Paper
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Product details 304 pages Dover Publications - English 9780486656335 Reviews:
"Synopsis" by ,
Covers sets and functions, groups, metric spaces, topologies, topological groups, compactness and connectedness, function spaces, the fundamental group, the fundamental group of the circle, locally isomorphic groups, more. 1967 edition.
"Synopsis" by ,
"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.

"Synopsis" by ,
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.

 

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