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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