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Simmons G.F. — Introduction to topology and modern analysis
Simmons G.F. — Introduction to topology and modern analysis



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Название: Introduction to topology and modern analysis

Автор: Simmons G.F.

Аннотация:

This material is intended to contribute to a wider appreciation of the mathematical words "continuity and linearity". The book's purpose is to illuminate the meanings of these words and their relation to each other.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 372

Добавлена в каталог: 03.03.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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