Köthe G. — Topological vector spaces I :: Электронная библиотека попечительского совета мехмата МГУ

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Köthe G. — Topological vector spaces I

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Название: Topological vector spaces I

Автор: Köthe G.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 456

Добавлена в каталог: 24.09.2005

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Предметный указатель

$c_{0}$       131 302 333 335 343 425
      308 426
$H(\Gamma)$       421
$H(\mathfrak{D})$       375
$H(\mathfrak{G})$       372 ff. 432
$HB(\mathfrak{G})$       138 ff. 352
$l^{1}$       333 335 343 350 357
$l^{1}_{d}$       283 404 424
$L^{p}$       139 ff. 156 343 351 355 431
$L^{p}$ , 0<p<1,      156 160 195
$l^{p}(E_{n})$       359 360
$l^{p}_{d}$       137 359 431
$l^{p}_{n}$       137 429
$l^{\infty}$       142 333 343 347 352 357 425
$l^{\infty}_{d}$       283 363 424
$T_{2}$ -space      3
$\aleph_{\alpha}$ -compact      18 315
$\alpha$ -dual      405
$\beta$ -dual      423
$\mathbf{P}$ , $\mathbf{P}^{n}$       5
$\mathbf{P}^{\omega}$       8
$\mathfrak{M}(K)$ , $\mathfrak{M}(R)$       138 324 333 339 343 347
$\mathfrak{P}^{A}$       8
$\mathfrak{T}^{f}$       267 ff. 269 271
$\mathfrak{T}^{lf}$       267 ff. 269 271
$\mathfrak{T}^{\circ}$       266 271
$\mathfrak{T}^{\times}$       380
$\mathfrak{T}_{b*}$       262 263 283 286 398
$\mathfrak{T}_{b}$       256 257 263 277 285 286 300 370 385 400 436
$\mathfrak{T}_{c_{0}}$       385 ff.
$\mathfrak{T}_{c}$       263 264 273 278 385 389
$\mathfrak{T}_{k}$       98 260 263 277 278 282 285 286 293 302 325 385
$\mathfrak{T}_{lb}$       115
$\mathfrak{T}_{lk}$       97
$\mathfrak{T}_{ls}$       86 ff. 238
$\mathfrak{T}_{n}$       300
$\mathfrak{T}_{p}$       323
$\mathfrak{T}_{s}$       234 238 248 276 277 285 286 354
$\mathfrak{T}_{\mathfrak{M}}$       255 266
$\omega$ , $\omega_{d}$       56 70 75 119 122 151 155 243 248 268 287 391 406 431 432
$\omega\varphi$       119 120 121 431
$\omega\varphi\oplus\varphi\omega$       304 370
$\Psi$       109 122
$\sigma$ -additive measure      426
$\varphi$ , $\varphi_{d}$       53 70 76 122 214 268 287 308 370 406 431
$\varphi\omega$       119 120 431
$\varphi\omega\oplus\omega\varphi$       120 ff. 240 296 304 370
(B)-space      126 250 252 273 280 283 303 304 315 335 336 389 401 431
(DF)-space      396 ff. 401 434
(F)-norm      163 ff.
(F)-space      164 205 225 265 273 278 303 306 309 315 318 371 388 389 393 399 400 431
(FK)-space      424
(FM)-space      369 373 433
(LB)-space      223 ff. 434
(LF)-space      223 ff. 384
(M)-space      369 421 434
Absolute bipolar      246 249
Absolute polar      245
Absolutely convex      160 173 203
Absolutely convex about a point      175
Absolutely convex cover      173 ff. 240 325
Absolutely p-convex      160
Absolutely p-convex cover      160
Absorb      301
Absorbent      145
Accumulation point      4
Adherent point of a filter      12
Adherent point of a net      10
Adjoint mapping      73 197 237
Alaoglu — Bourbaki theorem      248 264
Alaoglu, L.      248
Alexandroff s theorem      21
Alexandroff, P.      21
Algebra      59
Algebraic basis      51 194
Algebraic boundary      177
Algebraic boundary point      177
Algebraic complement      51
Algebraic conjugate      69
Algebraic dimension      53 75
Algebraic dual      69 ff. 88 97 1O1 247
Algebraic hull      177
Algebraic interior point      177
Algebraic kernel      177
Algebraic point of smoothness      345
Algebraically closed      177 193 194
Algebraically closed convex $\alpha$ -body      see “Convex $\alpha$ -body”
Algebraically closed half space      179 ff.
Algebraically isomorphic      53
Algebraically open      177
Algebraically open half space      179 ff.
Allen, H.S.      423
Almost constant sequence      89
Amemiya, I.      384 404 405 436
Anti-isomorphic      65
antisymmetric      9
Arens, R.F.      260 335
Associated bornological space      380
Asymptote      341
Automorphism      60
Baire, R.      27
Baire’s theorem      27
Ballier, F.      121
Banach algebra      130
Banach space      126
Banach — Dieudonne theorem      252 254 272
Banach — Mackey theorem      252 254
Banach — Schauder theorem      166
Banach — Steinhaus theorem      169
Banach — Stone Theorem      334
Banach, S.      165 168 170 189 259 272 350 431
Banach’s theorem      169
Barrel      257
Barrelled      257 261 297 305 306 367 369 371 372 380 434
Base of a uniform space      30
Base of neighborhoods      3
Basis of open sets      1
Bessaga, C.      166
Bidual      129 196 298 300 388
Bidual space      see “Bidual”
Bilinear form      78
Bilinear functional      78
Bilinear mapping      78 171
Bipolar      246
Birkhoff, G.      11
Bohnenblust, H.F.      192
Boolean algebra      58
Bornological      379 ff. 387 388 399 400 403 419 434 436
Boundary      4
Boundary point      4
Bounded      24 152 248 254 403
Bounded above      9
Bounded below      9
Bounded closure      386 ff. 401
Boundedly closed      386 ff. 400
Bourbaki, N.      1 12 20 76 121 172 173 186 188 211 233 260 312 332 357 366 427 431 434
Bourbaki’s theorem      172
Bourgm, D.G.      159 162
Braconnier, J.      233
BV(I)      425
C      131
C(K), C(R)      138 250 323 334 335 343 350
Canonical mapping of E onto E/H      60
Canonical representation in the narrow sense      67
Canonical representation in the wide sense      67
Cantor, G.      25
Cartesian product      8
Cauchy filter      32 210
Cauchy net      32
Cauchy sequence      25

CHARACTER      309
Characteristic function      41
Chillingworth, H.R.      423
Circled      146
Circled cover      146 174 241
Civin, P.      304
Clarkson, J.A.      353 357
Close of order N      29
Closed      321 322
Closed absolutely convex cover      175 (see also “Absolutely convex cover”)
Closed absolutely convex set      see “Absolutely convex”
Closed ball of radius r      24
Closed convex cover      175 (see also “Convex cover”)
Closed convex set      see “Convex”
Closed graph theorem      167
Closed linear subspace      see “Linear subspace”
Closed mapping      6
Closed set      1
Closure      4
Closure point      4 312
Co-dimension      55
Co-echelon space      419 433
Co-echelon space, p-th order      420
Co-nullity      67
Coarser filter      12
Coarser topology      5
Coarser uniformity      30
Cofinal      10
Cofinal subnet      10
Collins, H.S.      269 271
column      63
Column-finite matrix      63
Compact      16 ff. 154 241 279 313 326 331 336 340 385 415
Compactum      26
Compatible      82 145
Compatible linear topology      236
Compatible locally convex topology      236 245 254 261
Complement of the image space      60
Complementary subspaces      51 95
Complemented lattice      58
complete      25 32 165 210 231 269 402 435 “Sequentially
Complete in itself      252
Complete lattice      57 85
Complete metric space      25 42
Complete metrizable vector space      166 ff. 172
Completely regular      45 47
Completion of a Hausdorff uniform space      33
Completion of a linearly topologized space      115 149
Completion of a locally convex space      208 248 261 269
Completion of a metric space      25
Completion of a topological vector space      148 158
Complex hyperplane      180
Complex linear functional      179
Complex locally convex space      273 ff.
Complex vector space      49
Cone      183 ff. 195 337
Cone generated by a set      184
Conjugate space      86 128
Connected      5 152
continuous      6
Continuous basis      101
Continuous bilinear mapping      171
Continuous dimension      101 102
Continuous linear functional      156 158
Continuous linear mapping      98 129 148 166 167 237 262 291 297 333 381
Continuous projection      see “Projection”
Converge      10 12
Convergent sequence of matrices      107
Convex      160 173 186 194 244 273 322 336 337 343
Convex $\alpha$ -body      180—194
Convex $\mathfrak{T}$ -body      180 182 187 188 193 342
Convex algebraic body      see “Convex $\alpha$ -body”
Convex cover      173 ff. 240 245 321 322 325 331
Convex function      181
Convex-compact (weakly)      316
Cooke, R.G.      423
Cooper, J.L.B.      424
Coordinate space      405
Countability axioms      19 20
Countable at infinity      22
Countable degree      120 370
Countably compact      19 310 315
Cudia, D.      366
C[I]      138 197 260 430
Day, M.      157 317 318 360 361 363 366
Defect      55 67 103
Dense      4
Density zero      369
Diagonal      29
Diagonal transform      408
Diameter of a set      24
Diametrically opposite cone      183
Dieudonne, J.      48 85 113 121 272 274 311 318 354 369 370 371 372 384 387 404 419 421 424 432
DIMENSION      see “Algebraic dimension” “Continuous
Direct product      76
Direct sum      54 57
Directed set      9
Discrete topology      4 82 83
Discrete uniformity      31
Distance between two points      23
Distance between two sets      24
Distinguished      306 ff. 399 400 435
Distributive lattice      58
Dixmier, J.      304 336 426
Donoghue, W.F.      392
Dual      86 128 275 298
Dual pair      85 234
Dual space      see “Dual”
Dual system      70
Dually isomorphic lattices      57
E-bounded      251 254
Eberlein, W.F.      313
Eberlein’s theorem      313 317 326 366 415
Echelon space      419 433
Echelon space of p-th order      420
Eidelheit, M.      187
Embedding      60
Endomorphism      59
Equicontinuous      168 172 258 259
Equicontinuous bilinear mapping      171 ff.
Equivalent base of neighbourhoods      3
Equivalent defining system      216 227
Equivalent filter bases      12
Equivalent in the narrow sense      67
Equivalent in the wide sense      68
Equivalent linear mappings      67
Equivalent norms      125
Equivalent system of equations      105
Equivalent uniform spaces      30
Erdoes and Kaplansky’s theorem      75
Erdoes, P.      75
Essential supremum      142
Essentially bounded      142
Euclidean space      23
Everywhere dense      4
Exposed point      337
Exposed ray      341
Extension of a linear functional      70 86 188 233
Extension theorem      see “Preceding entry”
Exterior point      4
Extreme point      330 337 338 340 346
Extreme ray      337
Fan, K.      366
Fantappie, L.      373
Fichtenholz, G.      425 427
Filter      11
Filter corresponding to a net      11
Filter-base      12
Finer filter      12
Finer topology      5

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