INDEX OF TERMINOLOGY 355 cup, 55 cyclic group, 341 decimal expansion, 29 Dedekind cut, 24 degree of a polynomial, 296 degree of a representation, 233 delta measure, 193, 200 DeMorgan’s laws, 40, 276, 277 dense, 133 dense set, 5, 60, 63, 66, 81, 89, 123, 220, 245 derivative, 142, 146, 147, 149–154, 157, 158, 160–162, 167, 176 diagonal matrices, 344 diameter, 43, 118, 187 Dieudonn´ e, Jean, 191 difference of sets, 274 differentiable, 142, 149, 150, 168, 191, 192 dihedral group, 346 dimension of a vector space, 318 Dini’s theorem, 58, 83 direct sum, 234 directional derivative, 150, 151, 155, 156, 163 Dirichlet kernel, 242, 264 Dirichlet’s theorem, 7 disconnected set, 61 discontinuity, 243, 264, 265 discontinuous, 243 discrete metric, 35, 38, 40–42, 48, 56, 62, 80, 200 discrete topology, 65, 74, 102, 248 disjoint sets, 274 distance between sets, 58, 177 divergent series, 26, 76 divisibility, 285 divisor, 285 domain of a function, 292 Dominated Convergence Theorem, 212–214, 216 dot product, 334 dual basis, 121 dual group, 247, 250, 251, 259, 261 dual space, 108, 109, 114, 117, 130 Egorov’s theorem, 207, 208, 215 eigenspace, 137, 140 eigenvalue, 137 eigenvector, 137, 140 element of a set, 272 empty set, 272 endpoints of a rectangle, 184, 185 entire function, 255 epimorphism, 343 equality of sets, 272 equicontinuous, 93 equivalence class, 286 equivalence relations, 284 essential supremum, 217 essentially bounded, 217 Euler’s theorem, 30 even permutation, 326 eventually constant sequence, 45, 86 Exchange Lemma, 317 face of a rectangle, 185 factorial, 284 Fatou’s lemma, 211, 213, 215, 219 field, 288 field of rational functions, 73 finite complement topology, 65 finite field, 19, 89 finite rank operator, 138 finite set, 298, 302 finite-dimensional representation, 233 finite-dimensional vector space, 317 first category, 80 fixed point, 78 Fourier coefficient, 239 Fourier inversion, 249, 251, 252, 254, 256 Fourier series, 238, 239, 263 Fourier transform, 238, 242, 248, 251, 252, 261 Fr´ echet, Maurice Ren´ e, 271 Fubini’s theorem, 204, 220–224, 239, 240, 253 function equality, 292 fundamental counting principle, 278 Fundamental Theorem of Algebra, 71, 72 Fundamental Theorem of Calculus, 145 general linear group, 341, 344 generalized Cantor set, 80 generalized limit, 114, 116, 229 Generalized Mean Value Theorem, 145 generalized rotation, 347 geometric series, 26 Gibbs phenomenon, 264, 265 glb, 306 global maximum, 166 global minimum, 166 gradient vector, 155, 164, 171
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