354 INDEX OF TERMINOLOGY Bounded Inverse Theorem, 110–112 bounded linear functional, 108, 117 bounded linear operator, 79, 106, 237, 269 bounded sequence, 10, 14, 21 bounded set, 2, 21, 48, 57 bounded variation, 52 Bourbaki, Nicolas, 33 canonical basis, 317 Cantor function, 53, 202 Cantor set, 16, 53, 80, 185, 202, 206 cap, 55 cardinal number of a finite set, 298 Cartesian product, 278 Cartesian product of groups, 346 Cartesian product of sets, 277 Cauchy criterion, 14, 21 Cauchy sequence, 10, 14, 21, 44 Cauchy’s Mean Value Theorem, 145 Cauchy-Riemann equations, 158 Cauchy-Schwarz inequality, 127, 128, 132, 181, 217, 244, 246 center of a group, 125, 126, 231 center of a pair of vectors, 118, 119 chain rule, 144, 153, 154 change of variables, 224, 226, 227, 230, 232 character, 246, 265 character group, 246, 250 characters, 240 Chevalley, Claude, 313 choice function, 306 classical compact groups, 125, 126 classical groups, 124 closed ball, 20, 62 closed convex hull, 43 Closed Graph Theorem, 110, 111 closed map, 96 closed rectangle, 181, 184, 185 closed set, 16, 21, 39, 41, 57, 65 closed subgroup, 98, 99, 123, 124 closed subspace, 105, 233 closed unit ball, 40 closure, 41, 42, 65, 98, 228, 267 Cobb-Douglas production function, 173 coeﬃcients, 322 commutative algebra, 323 commutative ring, 289 commutative ring with identity, 87, 288 compact abelian group, 238, 251 compact group, 232, 246, 248 compact metric space, 77 compact open topology, 247, 248, 260 compact operator, 136, 138–140 compact set, 17, 56, 57, 59, 70 compact topological group, 98 compactly supported function, 103, 189, 220, 248, 255, 261 comparison test, 27 complement, 39, 275 complete independence of axioms, 310 complete measure, 200 complete metric space, 45, 47, 78, 103 complete ordered field, 72, 76 complete reducibility, 234 completion of a metric space, 63, 86 complex conjugate, 19 complex differentiable, 158 complex numbers, 19 complex power series, 28, 158, 163 component function, 154, 177 composite number, 285 composition of functions, 144, 292 congruence, 285 congruence modulo n, 308 conjugate, 94 conjugate exponent, 217 conjugate linear, 127 connected component, 62 connected set, 61, 159, 160 connected topological space, 97 consistent, 310 constant function, 291 constraint, 170, 171, 173–175 continuity of measure, 194 continuous function, 47, 48, 57, 61, 66, 70, 205 continuously differentiable, 147, 241 contraction mapping, 78, 79 Contraction Mapping Theorem, 78, 79 convergent infinite series, 133, 240 convergent sequence, 10, 13, 20, 44 convergent series, 26, 89 convex hull, 43 convex set, 43, 59, 61, 128, 163, 164, 177 convolution, 239, 248, 253, 256 coset, 89, 97 countable, 301 countable Cartesian product, 303 countably additive, 193, 198 countably infinite, 303 countably subadditive, 195, 196 counting measure, 193, 200, 216, 249 critical point, 167–171 cross product, 336

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