Montgomery D., Zippin L. — Topological transformation groups :: Электронная библиотека попечительского совета мехмата МГУ

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Montgomery D., Zippin L. — Topological transformation groups

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Название: Topological transformation groups

Авторы: Montgomery D., Zippin L.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1955

Количество страниц: 289

Добавлена в каталог: 11.11.2012

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

Предметный указатель

$E_{1}$       3
$E_{n}$       5
$GL_{n}$       21 50 71
$G_{x}$       43
$K_{0}$       129
$M_{n}$       20 50 72
$R_{1}$ , closed unit-interval      2
Abelian (-commutative) groups      20 83 101 187
Adjoint (representation)      106 149
Analytic coordinates      169
Analytic coordinates, analytic group (Lie)      49 68 169
Analytic coordinates, analytic structure (manifold)      45
ARC      2
Automorphism      22
Basis (for open sets)      3
Basis (for open sets), basis at e      25
Bounded metric      13
Brouwer theorem (invariance of n-cell)      176
Cantor diagonalizing procedure      14
Cantor discontinuum (Middle-Third set)      6 7
Carrier      86
Category      9 197
Cauchy criterion      14
Center      40
Center, central      39
Characteristic function, number      97
Class $C^{r}$       45 164
Class $C^{\infty}$       164
Closed, closure ( $\bar{ }$ )      4
Compact      6
Compact, locally compact      8
Complement (set)      4
Complete regularity      29
Complete space      14
Complex analytic structure      46
Complex analytic structure, complex homeomorphism      214
Component      37
Component of the identity      39
Conjugate (element, subset, subgroup)      39
Connected      39
Connected, locally      185
Connected, simply      46
Continuous (map)      4
Continuum (= compact, connected set)      37
Convergence (of points, $x_{n} \rightarrow x$ , $lim x_{n} = x$ )      14
Convergence of sets ( $lim A_{n} = A$ )      15
Coordinates of second kind      163
Coordinates, admissible      45
Coordinates, canonical of first kind      162
Coordinates, coordinate neighborhood      45
Coset for local groups      33
Coset, coset-space      26
Countability axioms      3
Cover (by open sets)      8
Cover (by open sets), covering-map      46 234
Cross-section, local      159 219
Decomponsition space (orbit-space)      61
Deformable (shrinkable, homotopic) to a point      234
Dense, everywhere      14
Dense, nowhere      9
Diagonal process, Cantor      14
Differentiable coordinates structure      45 164 196
DIMENSION      176
Direct decomposition, factor, summand (of groups)      20
Disconnected, totally      37 56
Discontinuum, Cantor      6 7
Discrete      2
Disjoined, disjunct      38
Dyadic (group)      48
Dyadic (group), dyadic rationals      28
e (identity of group, also subgroup consisting of identity)      19
Effective (transformation group)      40
Euclidean, locally      44
Exponential map      72 144
Factor (of a product)      20
Factor (of a product), factor-group      27
Faithful representation      190
Free subset (of $E_{n}$ )      247
Fundamental differential equations of a group      171
g.l.b.      8
Generating (subset of a group)      54
Generating (subset of a group), sequences of sets      108
Generator (of dyadic group)      49
Geodesic metric      216
Geometry of three-space      269
Group (axioms)      19

Group (axioms), product of groups      19
Group (axioms), subgroup      19
Group (axioms), topological      19
Group (axioms), transformation      40
Hausdorff metric      17
Hausdorff space      8
Hilbert fifth problem      67 184
Homeomorphism      2
Homogeneous space      30
Homomorphic, homomorphism      23
Homotopic path, homotopic to a point      234
I (the positive integers), I', I", I*, . . .      14
Identity e      19
Identity-component      39
Index (Brouwer)      252
Induced (relative) topology      4
Inner point      8
integral      85
Invariant (subset of a group)      22
Invariant (subset of a group), metric      34
Inverse set (map)      4
Inverse set (map) in a group      22
Inverse set (map), Isomorphism      22
Kernel (function)      97
Kernel (function) of a homomorphism      24
Lie group      49
Limit, projective      59
Limit, sequential      14 15
Local Group      31
Manifold      44
MAP      4
Map, natural      26
Matrix group (subgroup of $Gl_{n}$ )      71
Metric      12
Metric, invariant      34
Natural map      26
Neighborhood      8
Neighborhood of identity      25
Newman theorem      223
Normal space      38
Normal subgroup (— invariant subgroup)      22
One-parameter group      24 105 192
One-parameter group, semigroup of sets      110
Onto (map)      4
Open (map)      4
Open (set)      1
Open in (relative topology)      4
Orbit, orbit-space      61
Path      234
Periodic, pointwise periodic      222
Prod. $S_{\alpha}$ , product of spaces      5
Product of subsets of a group      20 22
Projective limit      59
Regular      9
Relative (induced) topology      4
Separable space (= 2nd countability)      17
Set, set-intersection: $\cap$ , set-union: $\cup$       1
Set-inverse (map)      4
Set-inverse (map), set-product in groups      22
Shrinkable to a point      234
Simple closed curve      2
Solenoid      66
Space      1
Sphere $S_{r}(A)$       15
Sphere $S_{r}(x)$       12
Stability group: $G_{x}$       40 64
Structural constants      170
Subbasis      3
Subgroup, closed      19
Subgroup, open      2 3
Symmetric (sets)      22
Symmetric (sets), neighborhood of e      25
Topological equivalence (homeomorphism)      2
Topological equivalence (homeomorphism), product      5
Topological equivalence (homeomorphism), space      1
Topological equivalence (homeomorphism), topological group      19
Totally disconnected groups      56
Transformation group      40
Transitive      30 43 63
Translation (left, right)      23
Translation (left, right) of euclidean three-space      268
Tychonoff theorem      9
Vector-addition, $x \circ y$       144
Vector-addition, x — y      146
Vector-space $V_{n}$       83
Wildly-imbedded      229
Without fixed points      235

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