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This book builds upon the revolutionary discovery made in 1974 that when one passes from function f to a function J of paths joining two points A1A1 the connectivities R1 of the domain of f can be replaced by connectivities R1 over Q, common to the pathwise components of a basic Frechet space of classes of equivalent curves joining A1 to A1. The connectivities R1, termed "Frechet numbers," are proved independent of the choice of A1 A1, and of a replacement of Mn by any differential manifold homeomorphic to Mn.

Originally published in 1976.

The Princeton Legacy Library...

The description for this book, Topological Methods in the Theory of Functions of a Complex Variable. (AM-15), Volume 15, will be forthcoming.

This book builds upon the revolutionary discovery made in 1974 that when one passes from function f to a function J of paths joining two points A1A1 the connectivities R1 of the domain of f can be replaced by connectivities R1 over Q, common to the pathwise components of a basic Frechet space of classes of equivalent curves joining A1 to A1. The connectivities R1, termed "Frechet numbers," are proved independent of the choice of A1 A1, and of a replacement of Mn by any differential manifold homeomorphic to Mn.

Originally published in 1976.

The Princeton Legacy Library...

From the Introduction: Marston Morse was born in 1892, so that he was 33 yearsold when in 1925 his paper Relations between the critical points of a real-valuedfunction of n independent variables appeared in the Transactions of theAmerican Mathematical Society. Thus Morse grew to maturity just at thetime when the subject of Analysis Situs was being shaped by such masters asPoincare, Veblen, L. E. J. Brouwer, G. D. Birkhoff, Lefschetz and Alexander, and it was Morse's genius and destiny to discover one of the most beautifuland far-reaching relations between this fledgling and...