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Авторизация |
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Montgomery D., Zippin L. — Topological transformation groups |
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Предметный указатель |
3
5
21 50 71
43
129
20 50 72
, 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 45 164
Class 164
Closed, closure () 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, , ) 14
Convergence of sets () 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 ) 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 ) 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. , 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: , set-union: 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 15
Sphere 12
Stability group: 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, 144
Vector-addition, x — y 146
Vector-space 83
Wildly-imbedded 229
Without fixed points 235
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