TABLE OF CONTENTS
Chapter I . Linear maps . 1
§1. Calibration . 3
§2. T-continuous maps. 5
§3. T-bounded elements. 10
§4. T-open subsets . 18
Chapter I I . Differentiation . 21
§1. Definitions. 22
§2. Elementary properties . 26
§3. Chain r u l e s . 33
Chapter I I I . Inverse mapping theorem. 36
§1. T-balanced subsets . 36
§2. r_contractions. 37
§3. Differentiabilit y of inverse maps. 40
§4. Stric t d i f f e r e n t i a b i l i t y . 41
§5. Inverse mapping theorems. 44
Chapter IV. Differentia l equations. 47
§1. Restriction s to Bp(E). 47
§2. Some spaces of continuous functions. 48
§3. Existence theorems. 52
Chapter V. Fredholm maps. 57
§1. Splittin g maps. 58
§2. C r i t i c a l s e t s . . 61
§3. Fredholm maps. 62
Chapter VI. Analytic maps. 67
§1. T-polynomials. 69
§2. Local T-boundedness. 70
§3. T-analytic maps. 71
§4. Br-analytic maps. 73
Appendix. Manifolds. 76
References. 80
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