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First Concepts of Topology: The Geometry of Mappings of Segments, Curves, Circles, and Disks
 
First Concepts of Topology
MAA Press: An Imprint of the American Mathematical Society
eBook ISBN:  978-0-88385-933-9
Product Code:  NML/18.E
List Price: $50.00
MAA Member Price: $37.50
AMS Member Price: $37.50
First Concepts of Topology
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First Concepts of Topology: The Geometry of Mappings of Segments, Curves, Circles, and Disks
MAA Press: An Imprint of the American Mathematical Society
eBook ISBN:  978-0-88385-933-9
Product Code:  NML/18.E
List Price: $50.00
MAA Member Price: $37.50
AMS Member Price: $37.50
  • Book Details
     
     
    Anneli Lax New Mathematical Library
    Volume: 181966; 160 pp

    The authors of First Concepts of Topology demonstrate the power, the flavor and the adaptability of topology, one of the youngest branches of mathematics, in proving so-called existence theorems. An existence theorem asserts that a solution to some given problem exists; thus it assures those who hunt for a solution that their labors may not be in vain. Since existence theorems are frequently basic to the structure of a mathematical subject, the applications of topology to the proofs of these theorems constitute a unifying force for large areas of mathematics.

    In Part I of this monograph an existence theorem governing a large class of one-dimensional problems is treated; all the important ingredients in its proof, such as continuity of functions, compactness and connectedness of point sets, are developed and illustrated. In Part II, its two-dimensional analogue is carefully built via the necessary generalizations of the one-dimensional tools and concepts. The results are applied to such fundamental mathematical objects as zeros of polynomials, fixed points of mappings, and singularities of vector fields.

  • Table of Contents
     
     
    • Chapters
    • Part I. Existence Theorems in Dimension 1
    • Part II. Existence Theorems in Dimension 2
  • Reviews
     
     
    • This book is devoted to the popularization of some basic notions and results of topology ... Before stating and proving the appropriate theorems, the notions of continuity, compactness, connectedness, winding number, etc. are discussed in a leisurely and instructive manner. ...

      M. Edelstein, Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 181966; 160 pp

The authors of First Concepts of Topology demonstrate the power, the flavor and the adaptability of topology, one of the youngest branches of mathematics, in proving so-called existence theorems. An existence theorem asserts that a solution to some given problem exists; thus it assures those who hunt for a solution that their labors may not be in vain. Since existence theorems are frequently basic to the structure of a mathematical subject, the applications of topology to the proofs of these theorems constitute a unifying force for large areas of mathematics.

In Part I of this monograph an existence theorem governing a large class of one-dimensional problems is treated; all the important ingredients in its proof, such as continuity of functions, compactness and connectedness of point sets, are developed and illustrated. In Part II, its two-dimensional analogue is carefully built via the necessary generalizations of the one-dimensional tools and concepts. The results are applied to such fundamental mathematical objects as zeros of polynomials, fixed points of mappings, and singularities of vector fields.

  • Chapters
  • Part I. Existence Theorems in Dimension 1
  • Part II. Existence Theorems in Dimension 2
  • This book is devoted to the popularization of some basic notions and results of topology ... Before stating and proving the appropriate theorems, the notions of continuity, compactness, connectedness, winding number, etc. are discussed in a leisurely and instructive manner. ...

    M. Edelstein, Mathematical Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.