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| Авторизация |
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| Simmons G.F. — Introduction to topology and modern analysis |
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| Предметный указатель |
Hilbert space(s) Pythagorean theorem 249
Hilbert space(s) representation 260
Hilbert space(s) representation of functionals on 261
Hilbert's space-filling curve 341-342
Hilbert, D. 49
Hille, E. ix 232n
Holder's inequality 218
Holder's inequality general form 219
Holder's inequality, in relation to Cauchy's 219
Homeomorphic image 94
Homeomorphic spaces 94
Homeomorphism 93
Hopf, H. 130n
Hurewicz, W. 150
Ideal in algebra, contrasted with ring ideal 209
Ideal in algebra, maximal 314
Ideal in ring 184 185
Ideal in ring general significance 188—190
Ideal in ring maximal 190
Ideal, in algebra 209 313
Image, continuous 93
Image, homeomorphic 94
Induced functionals 231
Inequality, Bessel's 252—253 257
Inequality, Cauchy's 88 219
Inequality, Holder's 218 219
Inequality, Minkowski's 88 90 218 219
Inequality, Schwartz's 246
Inequality, triangle 51
Infimum 45
Infinite-dimensional Euclidean apace 90
Infinite-dimensional unitary space 90
Inner product 245
Interior 63 97
Interior point 63 97
Intervals 5 57
Involution 324
Isolated point 96
Isometric isomorphism 222
Isometry 79
Join 46
Joint continuity 118
Jordan, C. 341—342
Kadison, R.V. 269
Kakutani, S. 265n
Kamke, E. 42n
Kelley, J.L. 139n
Kellogg, O.D. 338
Kolmogorov, A.N. 128 215n
Kronecker delta 283
Kuratowski closure axioms 98
Laguerre functions 259
Lattice 46 344
Lattice characterization 344—345
Lattice complemented 345
Lattice complete 47
Lattice distributive 345
Lattice sublattice of 47
Laurent expansion 313
Least upper bound property 21 45
Lebesgue Covering Lemma 122
Lebesgue number 122
Lebesgue, H. 49
Legendre polynomials 259
Limit point 65 90
Limit point, contrasted with limit 72
Limit, in the mean 257
Limit, of sequence 50 70—71 132
Lindelof's theorem 100
Linear space 81 191
Linear space basis for 197
Linear space dimension 200
Linear space isomorphism 200
Linear space, linear combination in 194
Linear space, linear dependence in 196—107
Linear space, linear independence In 196—197
Linear space, linear operations in 191
Linear space, linear subspace(s) 81 193
Linear space, linear subspace(s) disjoint 195
Linear space, linear subspace(s) sum of 195
Linear space, linear subspace(s) sum of direct 195
Linear space, normed 54 81 212
Linear space, quotient space 193—194
Linear space, representation 201—202
Linear transformation(s) 203
Linear transformation(s) bound for 220
Linear transformation(s) bounded 220
Linear transformation(s) continuous 219 220
Linear transformation(s) idempotent 206
Linear transformation(s), identity 205
Linear transformation(s), inverse 205
Linear transformation(s), negative 204
Linear transformation(s), non-singular 205
Linear transformation(s), norm 220—221
Linear transformation(s), null space 207
Linear transformation(s), nullity 207—208
Linear transformation(s), product 204
Linear transformation(s), range 207
Linear transformation(s), rank 208
Linear transformation(s), scalar multiple 204
Linear transformation(s), zero 204
Linearly ordered set 44
Liouville's theorem 309—310
Lipschitz condition 339
Locally compact space 120 162
Locally connected space 151
Loomis, L.H. ix 215n 305n
Lorch, E.R. 296n
Lorentz, G.G. 157
Lower bound 44
Lower bound greatest 44—45
Mackey, G.W. 265n 305n
MacLane, S. 29
Mapping(s) see also “Function” 16
Mapping(s) bounded 58
Mapping(s) closed 342
Mapping(s) composition (multiplication) of 19
Mapping(s) continuous 70 93
Mapping(s) continuous at point 75—76 104
Mapping(s) continuous in single variable 118
Mapping(s) continuous jointly 118
Mapping(s) continuous uniformly 77
Mapping(s) contrasted with function 17
Mapping(s) equality for 20
Mapping(s) Gelfand 319
Mapping(s) graph 23
Mapping(s) identity 20
Mapping(s) into 17
Mapping(s) inverse 17
Mapping(s) isometric 79
Mapping(s) of sets 18—19
Mapping(s) one-to-one 17
Mapping(s) onto 17
Mapping(s) open 93
Mapping(s) product 19
Matrices, canonical form problem 286
Matrices, operations for 282—283
Matrices, similar 286
Matrix, as independent entity 281 284
Matrix, conjugate transpose 294
Matrix, determinant 287
Matrix, diagonal 287
Matrix, identity 283
Matrix, inverse 284
Matrix, non-gin gular 284
Matrix, of operator 281
Matrix, scalar 286
Matrix, triangular 205
Matrix, zero 283
Maximal element 44
| Maximal ideal space 319
Maximum 45
Maximum modulus theorem 311
McCoy, N.H. 172
Meet 46
Metric 51
Metric space 50 51
Metric space complete 71
Metric space completion 84-85
Metric space contraction in 338
Metric space sequentially compact 121
Metric space subspace of 56
Metric space totally bounded 123
Metrizable space 93
Minimum 45
Minkowski's inequality 88 90 218 219
Module 191n
Moments of a function 157
Morera's theorem 160 303
Multiplicative functional 321
Muntz's theorem 157
n-dimensional Euclidean space 87
n-dimensional unitary space 90
Naimark (or Neumark), M.A see also Gelfand — Neumark theorems ix
Natural imbedding 232
Neighborhood 96
Neumark see “Naimark”
Niven, I. 43
Norm(s) 54 81 212
Norm(s) equivalent 223
Norm(s) metric induced by 54 81 212
Norm(s) uniform 216
Normal operator 269
Normal space 133
Normed linear space 54 81 212
Normed linear space isometric isomorphism 222
Normed linear space locally compact 224
Normed linear space natural imbedding 232
Normed linear space non jugate space of 224
Normed linear space reflexive 232
Normed linear space representation 234
Normed linear space second conjugate space of 231
Normed linear space strong topology 232
Normed linear space weak topology 232
Normed linear space weak* topology 232—233
Nowhere dense set 74 99
Numbers, algebraic 43
Numbers, cardinal 31
Numbers, comparability theorem 48
Numbers, complex 23 52—54
Numbers, finite 32
Numbers, real 21
Numbers, transcendental 43
One-point compactification 163
One-to-one correspondence 18
Open base 99
Open base, for point (at point) 96
Open base, generated by open subbase 101
Open cover 111
Open cover basic 112
Open cover subbasic 2
Open cover subbasic of 111
Open mapping 93
Open mapping theorem 211 236
Open rectangles 101 119
Open set 60 91 92
Open set basic 99
Open set subbasic 101
Open sphere 59
Open strips 101
Open subbase 101
Open-closed set 349
Operator(s) 222
Operator(s) adjoint 263
Operator(s) characteristic equation 288—289
Operator(s) conjugate 241
Operator(s) determinant 28
Operator(s) eigenspace 278
Operator(s) eigenvalue 278
Operator(s) eigenvector 278
Operator(s) imaginary part 271
Operator(s) matrix 281
Operator(s) normal 269
Operator(s) projection(s), on Banach space 237
Operator(s) projection(s), on Hilbert space 274
Operator(s) projection(s), on Hilbert space orthogonal 276
Operator(s) real part 271
Operator(s) reduced by subspace 275
Operator(s) ring 303
Operator(s) self-adjoint 266
Operator(s) self-adjoint ordering 268
Operator(s) self-adjoint positive 268
Operator(s) spectral resolution 280 291
Operator(s) spectral resolution uniqueness 291—293
Operator(s) spectral theorem 280 290 295—297
Operator(s), spectrum 289 296
Operator(s), square root 294
Operator(s), subspace invariant under 275
Operator(s), unitary 272
Order relation, on real line 7
Order relation, partial 7 43
Order relation, total (or linear) 7 44
Origin 54 80 191
Orthogonal complement 249
Orthogonal dimension 259—260
Orthogonal vectors 249
Orthonormal basis 293
Orthonormal set 251
Orthonormal set complete 255
Parallelogram law 247
Parseval's equation 256 257
Partial order relation 7 43
Partially ordered set 43—44
Partition 26
Partition sets 26
Peano space 342n
Peano, G. 341—342
Perfect set 99
Permutation 176
Phillips, R.S. ix 232
Picard's theorem 339
Plane, complex 23 52—54
Plane, coordinate 22
Plane, Euclidean 22 87—88
Point, at infinity 162 163
Point, boundary 68 97
Point, fixed 338
Point, in a space 51 92
Point, interior 63 97
Point, isolated 96
Point, limit 65 96
Point, neighborhood of 96
Pointwise convergence 83
Pointwise operations 55 82 106
Product of sets 23—25
Product space 117
Product topology 116
Product topology, closed subbase 117
Product topology, open base 117
Product topology, open subbase 116
Projection 25
Projection on Banach space 237
Projection on Hilbert space 274
Projection on linear space 205—207
Proper value 278n
Proper vector 278n
Pseudo-metric 58
Pythagorean Theorem 249
Quotient, algebra 209
Quotient, ring 187
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