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