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 A1≠A1 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.
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Table of Contents:
- Frontmatter, pg. i
- Contents, pg. iv
- Introduction, pg. vii
- PART I. The Weierstrass integral J, pg. 1
- Part II. The Euler Equations, pg. 34
- Part III. Minimizing arcs, pg. 92
- PART IV. Preparation for Global Theorems, pg. 125
- PART V. Global Theorems, pg. 173
- Appendices, pg. 217
- Bibliography, pg. 244
- INDEX OF TERMS, pg. 252