First Concepts of Topology: The Geometry of Mappings of Segments, Curves, Circles, and Disks ^ heliiaruy + hyperlinkedToC pdf

First Concepts of Topology: The Geometry of Mappings of Segments, Curves, Circles, and Disks
By W. G. Chinn and N. E. Steenrod

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 an 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

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there is an unhyperlinked version out there. abandon all hope for it.


HERE i have uploaded it with very detailed linked Table of Contents

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he li i a ruy yur aii l e h