Index

Affine map, 115

Antipodal points, 138

Ball, 13

Banach space, 13

Barycenter, 125

Barycentric subdivision, 125

Base of a vector space generated by

a set, 24

Bilinear map, 18

Borsuk

theorem on odd maps, 192

Antipodensatz, 198

Borsuk-Ulam theorem, 198

Cauchy theorem (for operator-valued

integrands), 201

Central projection, 146, 147

Chain rule for differentials, 18

Codimension, 14

Co-kernel, 17

Compact set, 15

Complementary space, 13

Complete continuity, 15, 203

Complex extension of a linear "real"

operator, 205

Complexification of a real Banach

space, 204

Component of an open set, 23

Conjugation, 206

Connected set, 21

Convex

hull, 22

set, 21

Coordinate transformation, 100, 101

Cr-map,

19

Critical

point, 19

value, 19

Differential, 18

Direct

sum, 13

summand, 13

Dugundji extension theorem, 22

Eigenelement, 204

Eigenvalue:

definition, 203

generalized multiplicity of, 204

multiplicity of, 204

Extension theorem for odd

maps, 185

Face of a simplex, 115

Finite layer map, 28

7(M), definition of, 201

Fredholm alternative, 17

General position of a point set, 113

Generating set for a vector space, 24

Great circle, great sphere, 138

241