Items related to Topology: An Introduction with Application to Topological...
Topology: An Introduction with Application to Topological Groups (Dover Books on Mathematics) - Hardcover
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.
"synopsis" may belong to another edition of this title.
From the Back Cover
"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
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
"About this title" may belong to another edition of this title.
Search results for Topology: An Introduction with Application to Topological...
Stock Image
Topology: An Introduction With Application to Topological Groups (Dover Books on Mathematics)
Seller: POQUETTE'S BOOKS, DEWITT, MI, U.S.A.
Seller rating 4 out of 5 stars
Hardcover. Condition: Good. Seller Inventory # mon0000129618
Quantity: 1 available
Stock Image
Topology: An Introduction With Application to Topological Groups (Dover Books on Mathematics)
Seller: Once Upon A Time Books, Siloam Springs, AR, U.S.A.
Seller rating 4 out of 5 stars
hardcover. Condition: Good. This is a used book in good condition and may show some signs of use or wear . This is a used book in good condition and may show some signs of use or wear . Seller Inventory # mon0000777339
Quantity: 1 available
Stock Image
Topology: An Introduction With Application to Topological Groups (Dover Books on Mathematics)
Seller: HPB-Red, Dallas, TX, U.S.A.
Seller rating 5 out of 5 stars
Hardcover. Condition: Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority! Seller Inventory # S_435877693
Quantity: 1 available