Index of Terminology
C∞
function, 147, 162
Ck
function, 147, 162
T0 topological space, 67
T1 topological space, 67
T2 topological space, 67
T3 topological space, 67
T4 topological space, 67
σ-algebra, 192–199, 205, 209, 223
σ-algebra generated by a collection of
sets, 193, 223, 260
σ-finite measure, 200
σ-finite measure space, 194, 223, 224
m × n matrix, 322
n-sphere, 40
n-th root of unity, 23
p-adic absolute value, 85
p-adic completion of Q, 86
p-adic expansion, 90, 101, 247
p-adic field, 86, 94, 101, 194, 259
p-adic numbers, 94
abelian group, 341
absolute continuity of the integral, 213,
215, 216
absolute convergence, 241, 244
absolute value, 9, 13, 19, 74, 89, 94, 101
absolutely continuous, 246
absolutely continuous function, 51, 52,
202
absolutely convergent series, 27
accumulation point, 15, 22, 40, 65
adjoint operator, 116, 120, 121
affine subspace, 333
algebra, 323
algebra with identity, 323
algebraic closure, 71, 72, 76, 101
algebraic extension, 19, 71
algebraic number, 24, 72
algebraic of degree n, 148, 149
algebraically closed, 24, 72
almost everywhere, 182, 207
analytic function, 158, 255
angle between vectors, 335
antipodal points, 77
Archimedean ordered field, 4, 25
Archimedean property, 4
arithmetic-geometric mean inequality,
173
Arzela-Ascoli theorem, 93
associative, 293
associativity of composition of
functions, 293
automorphism group of a field, 18, 33,
101
automorphism of a field, 18, 94, 101
axiom, 310
axiom system, 310
Baire Category Theorem, 78, 81, 109
Banach algebra, 108
Banach space, 79, 103, 219
Banach, Stefan, 101
Banach-Steinhaus theorem, 110
base for a topological space, 66, 68, 198
basic additive character, 259, 260
basis, 121
basis of a vector space, 104, 155, 316
Bessel’s inequality, 132, 240, 244, 245
Big Hahn-Banach Theorem, 112–114
bijective function, 292
bilinear form, 334
binary operations, 288
binomial coefficient, 284
binomial theorem, 284
Bolzano-Weierstrass lemma, 14
Bolzano-Weierstrass theorem, 15, 22, 46
Borel measure, 199, 200, 205, 214, 260
Borel set, 198–201, 227, 238
Borsuk number, 77
boundary, 40, 42, 65, 187
boundary point, 40
bounded, 72
bounded above, 2, 72
bounded below, 2, 72
353
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