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
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