Margalef-Roig J., Outerelo Dominguez E. — Differential topology :: Электронная библиотека попечительского совета мехмата МГУ

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Margalef-Roig J., Outerelo Dominguez E. — Differential topology

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Название: Differential topology

Авторы: Margalef-Roig J., Outerelo Dominguez E.

Аннотация:

...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1

Год издания: 1992

Количество страниц: 618

Добавлена в каталог: 23.10.2010

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Предметный указатель

Operator of Fredholm      381
Orbits      301
Order of a quadrant      6
Origin map (s)      428
Orthogonal group      292
Outer tangent vector      68
p times differentiable maps      13
Paracompactness of manifolds      45
Parametrization by the arc-lenght      374
Partition of unity of class p      50
Partition of unity, existence      332
Partition of unity, subordinated to a covering      50
Path-connection in manifolds      43
Pointwise convergence topology      435
Primitive function      86
Product of Banach spaces      4
Product of differentiable manifolds      104
Product of embeddings      150
Product of equivalence relations      189
Product of immersions      147
Product of Lie groups      286
Product of Lie subgroups      290
Product of subimmersions      216
Product of submanifolds      147
Product of submersions      162
Product topology      435
Projective space (real)      33
Proper homotopy      461
Proper homotopy of class p      467
Property of Baire of $T_{s}$       453
Property of Baire of $T_{W}(p,p)$       484
Property of Baire of $T_{W}(\infty)$       494
Property of Baire of manifolds      44
Property of Lindeloef      42
Quadrant of a real Banach space      6
Quotient manifold      186
Quotient of Banach spaces      2
Quotient of equivalence relations      188
Rank of a differentiable map      64
Real projective spaces      33
Regular differentiable manifolds      45
Regular equivalence relation      185
Regular point      362
Regular value      363
Regulated function      85
Residual set      356
Retract of class $\infty$       257
Retraction of a manifold      235
Riesz's theorem      43
Right limit      85
Second axiom of countability      42
Second countable space      42
Second theorem of Sard (local)      370
Second theorem of Sard (manifolds)      371
Seeley's lemma      91
Semicontinuity of the rank      65
Separated duality      568
Sierpinski theorem      46
Singular point      398
Source map(s)      428
Space model of a chart      18
Space of Banach      2
Space of Hilbert      3
Space of k-jets      428 430
Space of k-multijets      551
Stabilizer      296
Step-function      85
Stiefel F-manifolds      34 213 304
Stiefel manifold      305
Strictily inner tangent vector      70
Strictily outer tangent vector      70
Strong topology      436
Structure differentiable in $J^{k}(X,X^{'})$       432
Structure differentiable of a quadrant      30
Structure differentiable on $B_{k}X$       29
Structure differentiable on a set      19
Subimmersion      215
Subimmersion at a point      215
Submanifold      113
Submanifolds of inverse images of a point by a subimmersion      224
Submanifolds of inverse images of subimmersion      224
Submanifolds of inverse images of submersions      174

Submanifolds of inverse images of transversal maps      319 225
Submersion      159
Submersion at a point      159
Subset of measure zero in $\mathbb{R}^{n}$       345
Subset of measure zero in manifolds      354
Subspace of a Banach space      2
Sum of manifolds      110 111
Tangent bundle manifold      66
Tangent linear map      63
Tangent space      63
Tangent to a map      9
Tangent vector      63
Tangent vector to a curve      68
Taylor's theorem      88 90
Theorem of Borel      486
Theorem of Brouwer      379
Theorem of Brown      372
Theorem of characterization of the subimmersions      229
Theorem of constant rank      234
Theorem of density of Abraham      413
Theorem of density of Quinn      403 408
Theorem of density of Smale      400
Theorem of density of the transversality      413 417 419 422
Theorem of density of the transversality in multijets      553
Theorem of embedding of Whitney      359 564 565
Theorem of extension of Whitney      80 99
Theorem of Fubini      352
Theorem of immersion of Whitney      359 559 562 565
Theorem of immersion of Whitney for compact manifolds      359
Theorem of Kneser — Glaeser      363
Theorem of local constant rank      225
Theorem of local representation      226
Theorem of Mather      553
Theorem of Sard      370 371 372
Theorem of Sard (elementary)      357
Theorem of Smale      400
Theorem of Taylor      88 90
Theorem of the fixed point      107 379
Theorem of the implicit function      108 109
Theorem of the implicit function (injective version)      131
Theorem of the implicit function (surjective version)      163
Theorem of the inverse function      100 101 103
Theorem of the mean value      12
Theorem of Thom      546
Topological group $Diff^{p}(X)$       521
Topological group of homeomorphisms      457
Topological linear space      2
Topological manifold      20
Topological supplement of a linear subspace      7
Topology $T^{k}$       430
Topology $T_{C^{0}}$       449
Topology in $J^{k}(X,X^{'})$       430
Topology of a differentiable manifold      21
Topology of a product of manifolds      105
Topology of a quotient manifold      186
Topology of a submanifold      115
Topology of graphs      436
Topology of Whitney      471 487
Totally neat submanifold      118
Transitive property of submanifolds      126
Transitivity of the transversality      321
Transversal family of maps      326
Transversal map to a submanifold      309 312 313
Transversal space to a submanifold      117
Transversal submanifolds      339
Transversality, local representation      324
Tubular neighbourhood, parcial      257
Tubular neighbourhood, total      257
Tychonoff's axiom      44
Uniform convergence topology      440
Uniform convergence topology over compact sets      435
Uniformity of a topological linear space      6
Uniformly closed subset      451
Unitary group      291
Unitary tangent bundle      360
Urysohn condition      50 51
Volume of a m-rectangle      345
Weak sum of manifolds      112
Weak topology of order $\infty$       487
Weak topology of order k      471
Weakned differentiable manifold      35
Whitney extension theorem      80 99
Whitney topology of order $\infty$       487

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