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Gordon Thomas Whyburn, "Topological analysis"

While the title "Topological Analysis" could embrace a wide range

of subject matter, including all phases of analysis related to topology or

derivable by topological methods, the material to be presented here

will be centered largely around results obtainable with the aid of the

circulation index of a mapping and properties resulting from openness

of a mapping. This choice of topics has been governed largely by the

special interests and tastes of the author, but it is hoped these may be

shared to an appreciable extent by others.

Organization of some of this material was begun in 1952-1953 while

the author held a Faculty Fellowship supported by the Fund for the

Advancement of Education of the Ford Foundation. It was further

aided by the author's participation in the University of Michigan conference

on Functions of a Complex Variable in the summer of 1953,

and some of the later work, especially that in Chapters V, VIII and X

involving new results, was supported in part by a grant from the National

Science Foundation (G 1132). The generous provision of a private study,

offering freedom from interruption, by the Alderman Library of the

University of Virginia during the past two sessions has greatly assisted

in bringing the book to conclusion. To all of these the author takes pleasure

in recording here an expression of his sincere gratitude. Thanks are due

also to the editors of the Princeton Mathematical Series for their interest

in the completed book and to the Princeton University Press for

its careful and sympathetic handling of the task of printing and

publishing it.

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