Akin E. — The Metric Theory of Banach Manifolds :: Электронная библиотека попечительского совета мехмата МГУ

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Akin E. — The Metric Theory of Banach Manifolds

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Название: The Metric Theory of Banach Manifolds

Автор: Akin E.

Аннотация:

This book describes the category of metric manifolds and metric maps to which a broad class of theorems and constructions extend from the realm of compact manifolds. The category is a broad one because all paracompact manifolds admit metric structures. Metric theorems include compact theorems because a compact manifold admits a unique metric structure and with respect to it any smooth map with compact domain is a metric map. Finally, there is a sufficient abundance of metric maps that, for example, structural stability under perturbation within the family of metric maps remains useful.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 306

Добавлена в каталог: 31.10.2008

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Предметный указатель

$comp_{H}$       35
$C^{\infty}$ metric structure      76
      50
      15
$f^{-1}$ is $\mathfrak{m}$       37
$G(\Phi, f)$       241
      62
$\delta^O(||\,||)$       97
$\delta^U(d)$ ( $= \delta^d(U)$ )      82
$\delta_U(d)$       84
$\Gamma(E)$ , $\gamma_E$ (canonical bundle)      234 241
$\kappa$       4 26
$\kappa(d)$       79
$\lambda$       4 26
$\Lambda$ choice      125
$\lambda^A_{(a_1,a_2)}$       197
$\lambda_a$       87
$\lambda_{(a_1,a_2)}$       193
$\mathfrak{m}_1$ maps $\mathfrak{m}_d$ to $\mathfrak{m}_r$ in an $\mathfrak{m}_2$ way rel $\mathfrak{m}_3$       29
$\mathfrak{m}_1\subset\mathfrak{m_2}$       16
$\mathfrak{n}(E)$ (space of norms)      55
$\mathscr{L}ip^r$ atlas      162
$\Omega_H$       29
$\theta$       1 174 175
a-chain      49
Accessory pseudometric (apm)      154
Atlas of normal coordinates      105
Bound      61
Bounded set      xi
C, $\overline{C}$       36 152
Com      146
COMP      3
Composition situation      115 171
Condition $\mathscr{L}$       99
Domination $(\succ)$       61
Embedding      195
Evaluation Property (FS8)      28
Factoring Lemma      202 207
Finite type      268 270
Finsler, $\zeta_U$ (and $\mathscr{L}$ )      293
Finsler, continuous      58
Frobenius theorem      253
Full neighborhood      82
G(f)      242
Gluing Property (FS5)      21
Group metric structure (on a B-space)      90
Identification at the atlas level      11 74
Index joke      304
Index preserving map      8
Integral Property (FS6)      22
Interchange Proposition      26
INV      5

Inv is $\mathfrak{m}$       38
Jet Lemma      24
Lamination Theorem      262
Li, $L\bar i$       174
Ls, $L\bar s$       175
Metric Estimate      51
Metricly proper map      155 191
Multi atlas      155
Munkres construction      269
n-tuple atlas      6
Norm metric structure (on a B-space)      72
O* notation      17
Open subbundle      182
Plaquation Theorem      254
Principal part (of a Finsler)      58
Principal part (of a map, section, fibre preserving map)      8
Product Property (FS7)      24
Refinement (of a metric structure)      70 90
Refinement (of an atlas)      6
Refinement, canonical      92
Regular (adapted atlas)      64
Regular (metric manifold)      68
Regular pseudometric space      77
Regularity lemma      91
Regularity, vertical      98
s-admissible      89
Scalarly $\mathfrak{m}$ map      27
Semicompact      89
Size Estimate      40
Smoothing Lemma      246
Smoothing Theorem      284
Split VB map      188
Square atlas      270
Standard function space type      36
Standard triple      115
Star-bounded cover, atlas      99
Strictly index preserving map      8
Strong inclusion      17
Strong Product Property (FS7 (strong))      24
Subdivision (of an a-chain)      50
Subdivision (of an atlas)      7
T isomorphism      102
Tangent Factoring Property      260
Tangent square      11
Transfer of atlas construction      7
Tranverse bounded set      78
Trimming (of a cover)      133
Truncation (of an a-chain)      50
u-star      86
Uniform cover      84
Vertical tangent subbundle      12
Vertically bounded      96

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