eBook ISBN:  9780883859339 
Product Code:  NML/18.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
eBook ISBN:  9780883859339 
Product Code:  NML/18.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 

Book DetailsAnneli Lax New Mathematical LibraryVolume: 18; 1966; 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 socalled 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 onedimensional 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 twodimensional analogue is carefully built via the necessary generalizations of the onedimensional 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


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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 socalled 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 onedimensional 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 twodimensional analogue is carefully built via the necessary generalizations of the onedimensional 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