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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