Granas A., Dugundji J. — Fixed Point Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Granas A., Dugundji J. — Fixed Point Theory

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Название: Fixed Point Theory

Авторы: Granas A., Dugundji J.

Аннотация:

This monograph gives a carefully worked-out account of the most basic principles and applications of the theory of fixed points. Until now, a treatment of many of the discussed topics has been unavailable in book form. The presentation is self-contained and is accessible to a broad spectrum of readers. The main text is complemented by numerous exercises, detailed comments, and a comprehensive bibliography.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 716

Добавлена в каталог: 05.04.2008

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Предметный указатель

$(n, \epsilon)$ -spanning set      490
$(\chi — n)$ -cohomology system      509 515
$E^{+}$ -cohomology      560
$E^{+}$ -compact field      560
$E^{+}$ -compact field, homotopy      560
$E^{+}$ -finite field      2
$E^{+}$ -finitely homotopic fields      563
$F^{*}$ -map      142
$F^{+}$ -etunpactly homotopic fields      560
$L^{p}$ -Carathoodory function      115 183
$L^{p}$ -Carathoodory function, solution      183 184
$R_{\delta}$ -map      550
$\alpha$ -close maps      134 282 467
$\alpha$ -contractive family      33
$\alpha$ -contractive family, map      12
$\alpha$ -contractive family, set-valued map      28
$\alpha$ -dominated space      134 468
$\alpha$ -field      494
$\alpha$ -fixed point      134 467
$\alpha$ -homotopic $\alpha$ -fields      494
$\alpha$ -homotopic $\alpha$ -fields, maps      282 467
$\beta$ -map      566
$\check{C}$ ech cohomology      495
$\check{C}$ ech cohomology, homology      411
$\delta$ -based $\epsilon$ -map      129
$\delta$ -orbit      22
$\epsilon$ -approximation      309
$\epsilon$ -chainable space      19
$\epsilon$ -coincidence point      537
$\epsilon$ -displacement      102
$\epsilon$ -fixed point      119
$\epsilon$ -map      102 129 546
$\epsilon$ -map in the narrow sense      129
$\epsilon$ -net      595
$\epsilon$ -normal map      556
$\lambda$ -slice      351
$\mathcal{F}$ -invariant set      172
$\mathcal{F}$ -map      488
$\mathcal{F}^{*}$ -homotopy      488
$\mathcal{G}$ -invariant set      44
$\mathcal{NB}$ -map      567
$\mathcal{N}\varepsilonS$ (compact metric)-map      465
$\mathcal{N}\varepsilonS$ (compact)-map      486
$\phi$ -map      176
$\varepsilon S$ (coinpact)-map      186
( $\epsilon; r)$ -isolating nbd      272
( $\epsilon; r)$ -isolating nbd, system      273
(T, k)-simple covering      554
(T, k)-simple covering, set      554
a priori bounds      346
A-proper map      366
Abelian group      608
Absolute neighborhood retract      279 304
Absolute retract      8 162 194 280 304
Absorbing set      426 601
Abstract complex      203 477
Acyclic decomposition      548
Acyclic decomposition, map      545
Acyclic decomposition, model theorem      404
Acyclic decomposition, set      35
Acyclic decomposition, set-valued map      542
Acyclic decomposition, space      421 531
Additivity      270 308 335 357 361 363 414 463 521
Adjoint functor      402
Admissible class      80 361 463
Admissible class, endomorphism      416
Admissible class, homotopy      5 291 552
Admissible class, Lefschetz space      572
Admissible class, map      552
Admissible class, space      141 470
Admissibly homotopic maps      120 291
Affine map      250
Affinely independent points      85
Alexander Kolmogoroff cohomology      412
Alexander Pontrjagin duality      509
Alexander Pontrjagin duality, invariance      513
Alexander Spanier cohomology      412
Alexandroff theorem      204
Algebraic multiplicity      327 606
Allowable extension      271
Allowable extension, map      339 367
Allowable extension, pair      485
Allowable extension, set      553
Almost periodic      48
Amenable group      50
ANR      279 304
ANR for normal spaces      357
ANR of type (W)      578
Antipodal map      87
Antipodal map, points      87
Antipodal map, theorem      14 93 99 104 106 135 191 269 321 352 358 525
Antipodal map, theorem for coincidences      136
Antipode-collapsing map      236
Antipode-preserving map      93 236
Approximate $\varepsilon S$ (compact)-map      186
Approximate $\varepsilon S$ (compact)-map, $\mathcall{N}\varepsilon S$ (compact metric)-map      466
Approximate $\varepsilon S$ (compact)-map, $\mathcall{N}\varepsilon S$ (compact)-map      487
Approximate $\varepsilon S$ (compact)-map, extensor spare      186
Approximate $\varepsilon S$ (compact)-map, neighborhood extensor space      472
Approximating family      468
Approximating family, sequence      100 185 500 563
Approximating family, system      501 563
Approximation theorem      135 354
ar      8 162 194 280 304
Arbitrarily small tails      32
Arens theorem      194
Arens — Eells theorem      597
Arzel $\grave{a}$ — Ascoli theorem      607
Associated Galerkin equation      158
Associated Galerkin equation, map and field      127 242
Asymptotic derivative      132
Asymptotically compact map      427
Asymptotically compact map, linear map      132
Asymptotically compact map, regular map      570
Attaching X to Y by f      294
Attracting set      426
Attractive fixed point      455
Attractor      22 77 426
Augmented functor-chain      404
b-map      176
Baire theorem      595
Baker’s transformation      78
Balanced set      601
Banach Alaoglu theorem      605
Banach Contraction Principle      10
Banach contraction principle, space      603
Banach contraction principle, theorem      603
Banach contraction principle, theorem, parametrized version      18
Banach — Mazur limit      50
Banach — Steinhaus theorem      604
Barycenter      200
Barycentric coordinate      86
Barycentric coordinate, coordinate system      477
Barycentric coordinate, refinement      597
Barycentric coordinate, subdivision      200
Base of topology      590
Base of topology of neighborhoods      591
Basic class      425
Basic class, (n-l)-cycle      208
Basic class, map      425
Basic class, triangulation      87
Basis of vector space      600
Basis of vector space of free group      610
Bernstein theorem      158
Betti number      222 373 376 405 565
Bicontinuous map      591
Bifurcation index      340
Bifurcation index, point      273 338 339
Bijective map      589
Bishop — Phelps theorem      27 32 35 36

BMO      583
Borsuk - Dugundji theorem      569
Borsuk - Ulam theorem      93 106
Borsuk - Ulam theorem, theorem, generalized      243 358 546
Borsuk extension theorem      287
Borsuk extension theorem, fibration theorem      296
Borsuk extension theorem, fixed point theorem      94 119
Borsuk extension theorem, homology embedding theorem      567
Borsuk extension theorem, metric      103
Borsuk extension theorem, presentation      566
Borsuk extension theorem, trace lemma      568
Bothe embedding theorem      301 437
Boundary map      612
Boundary map of set      590
Boundary map of simplex      86
Boundary map, operator      205 373
Boundary map, point      590
Boundary map, value problem      115 345 346
Bounded map      112
Bounded map, mean oscillation      582
Bounded map, set      594 601
Bounding cycle      215 219
Bowszyc theorem      230 432 451
Brouwer degree      234 246 363
Brouwer degree, theorem      95 106 108 137 138 140 186
Brouwer degree, theorem, generalized      545
Browder map      176
Browder — Caccioppoli theorem      361
Browder — Goehde — Kirk theorem      52 67
Bruhat — Tits theorem      50 80
Bundle      614
C-map      368
C-structure      368
Calculus of fractions      533
Cameron - Martin space      586
Canonical embedding      605
Canonical embedding, volume form      579
Cantor order-theoretic theorem      35
Cantor order-theoretic theorem, space      32
Cantor order-theoretic theorem, theorem      595
Caristi theorem      27
Carrier      101 198
Cartan theorem      490
Category      296 370 616
Category of direct systems      402
Category of endomorphisms      415
Category of fractions      533
Category of monomorphisms      415
Cauchy problem      180 183 184
Cell-like continuum      109
Cellular set-valued map      550
Centrally symmetric set      268
Chain      25 590
Chain, approximation met hod      159
Chain, complex      206 612
Chain, homotopic maps      210 404 613
Chain, homotopy      210 613
Chain, map      208 612
Chain, transformation      208
Characteristic of vector field      242
Characteristic of vector field, polynomial      223
Characteristic of vector field, rational function      436
Characteristic of vector field, value      322 606
Circled set      601
Class $C^{1}$       604
Closed embedding      591
Closed embedding, set      590
Closure      590
Coboundary homomorphism      564
Coboundary homomorphism, operator      613
Cochain complex      613
Cochain complex, map      613
Codifferential      613
Codimension      529 530 600
Coefficient group      492
Coercive bilinear form      66
Coercive bilinear form map      66 67
Cofiber      37 598
Cofibered pair      288
Cofinal subset      589 615
Cofunctor      371
Cohomological codimension      529
Cohomology functor      613
Cohomology functor, group      411
Cohomology functor, sequence of triple      496
Cohomology functor, theory      410 527 528
Cohomotopy group      525
Coincidence      143 538 547
Coincidence, degree      367
Coincidence, point      531
Coincidence, space      538
Cokernel      609
Collectively compact sequence      185
Combinatorial lemma      90
Commensurable subspaces      559
Commutative diagram      371 617
Commutativity      308 335 414 463
Compact attraction      427
Compact attraction, deformation      132
Compact attraction, field      127 139
Compact attraction, fraction      538
Compact attraction, homotopy      5 120 290
Compact map      112
Compact map, map of pairs      451 484
Compact map, set      593
Compact map, set-valued map      106 177 542
Compact map, space      593
Compactly absorbing map      427
Compactly absorbing map, extendable map      290
Compactly absorbing map, fixed homotopy      305
Compactly absorbing map, fixed map      305
Compactly absorbing map, homotopic maps      290
Compactly absorbing map, nullhomotopic map      290 292
Compactly absorbing map, rooted map      262
Compactum      540
Compatible family      402
Complementarity problem      76
Complementary subspaces      600
Complementing function      272
Complete metric      594
Complete metric, metric space      595
Complete metric, semilattice      31
Complete metric, simplex      101
Completely continuous map      112 544
Completing a diagram      617
Completion      595
COMPLEX      599
Component      590
Composite map      589
Composite map, morphism      370
composition      598 616
Composition, law      364
Concave family in the sense of Fan      42
Concave family in the sense of Fan, function      38
Concave-convex function      38
Concentrating      240
Condensing field      366
Condensing field, map      133 336
Cone      207 293 323 600
Cone, functor      514
Cone, operator      381
Conjugate space      42 604
Connected between A and B      319
Connected between A and B, space      590
Connecting homomorphism      613
Connectivity function      138
Consecutive pair of triads      498
Constant functor      403
Contiguous maps      479
Continuation method      12 33 192

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