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Авторизация |
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Morris S. — Pontryagin Duality and the Structure of Locally Compact Abelian Groups |
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Предметный указатель |
-space 78
24 27—40
, closed subgroups of 33
-space 6
-space 4
-space 4
Annihilator 90
Approximation by Lie groups 118
Approximation by metrizable groups 63
Arcwise connected 16
Ascoli's theorem 45
Baire category theorem 22
Banach space 14 48
Basis 33
Bohr compactification 88 101
Box topology 17 69
C(-, -) 43
Cardinality of character groups 96 102
Cartesian product 1 16
Character group 47
Character(s) 47
Character(s) enough 59—62 75 70 87 116
Character(s), extendability 66 91
Circle group 1
Closed subgroups of 36 94
Closed subgroups of 33
Closed subgroups of 36
Commutator subgroup 15 22
Compact element 97—99
Compact group, dual is discrete 50
Compact open topology 42
Compact torsion groups, characterized 69
Compact totally disconnected groups 21
Compactly generated 10 63 76 79 82 85 93 112
Component 11
Connected 10
Connected arcwise 16
Connected LCA-groups 11 53 86 99
Connected locally 106 110
Connected locally compact 118
Continuous homomorphism 7
Continuous metric 113
Countable locally compact groups 23 53 96
DIMENSION 106—111
Direct product 16 18 56 68
Direct product, restricted 17 67—69
Direct product, weak 17
Discrete group 1
Discrete group, dual is compact 50
Divisible group 18 34 100
Dual group 47
Dual group of an LCA-group is an LCA-group 49
Dual group of closed subgroups 57 90
Dual group of compact groups 50
Dual group of discrete groups 50
Dual group of finite groups 51
Dual group of products 56 67—69
Dual group of quotient groups 57 90
Dual group of R 48 51
Dual group of T 47 51
Dual group of Z 47 51
Duality theorem 53 65 84
Duality theorem for compact groups 65
Duality theorem for compactly generated LCA-groups 82
Duality theorem for discrete groups 66
Duality theorem for non-locally compact groups 68
Elementary group 71
Equicontinuous 44
Extendability of characters 66 91
Free Abelian group 33
Free abelian group, basis 33
Gelfand — Raikov theorem 116
General linear group 2
Group of automorphisms 25
Hausdorff space 4
Homogeneous 3
Indiscrete topology 1
Irreducible representation 116
Jointly continuous 43
| k-topology 42 49
Kronecker's approximation theorem 92
LCA-group 11
Lie group 105 118
Linear group 1
Locally compact fields 88
Locally compact group 9
Locally connected 106 110
Locally contractible 105
Locally Euclidean 105 111
Locally isomorphic 37—40 118
Locally isomorphic to 37
Matrix group 1
Maximally almost periodic 117
Metrizable 46 53 63 95 113
Monothetic group 71
No small subgroups 104 112 115
Non-discrete topologies on abelian groups 20
NSS-group 104 112 115
Open and closed subgroups 9
Open mapping theorem 23
Orthogonal group 2
Orthogonal matrix 2
P-topology 42 49
Paralleletope 29
Peter — Weyl — van Kampen theorem 62
Pontryagin — van Kampen duality theorem 53 84
Principal structure theorem 86
Product topology 17
Products 17 25
Projective limit 22
q 1
Quotient group 12
R 1
R, character group of 48 51
Rank 29 107—110
Real characters 21 87
Refine 107
Reflexive 68
Regular 6 45
Representation 116
Representation, finite-dimensional 117
Representation, irreducible 116
Representation, unitary 116
Restricted direct product 17 67—69
Semidirect product 25
Separate points 59—62 65 70 87 116
Solenoidal group 87 102
Special linear group 2
Special orthogonal group 2
Special unitary group 2
Structure theorem, Principal 86
Structure theorem, Principal for compact torsion groups 69
Structure theorem, Principal for compactly generated LCA-groups 85
Structure theorem, Principal for connected LCA-groups 86
Structure theorem, Principal for connected locally compact groups 118
t 1 47 51
Topological (group) isomorphism 7
Topological group 1
Topological group, compactly generated 10
Topological group, discrete 1
Topological group, monothetic 71
Topological group, quotient 12
Topological group, solenoidal 87
Topologically isomorphic 7
Topology of pointwise convergence 42
Torsion group, compact characterized 69
Torsion subgroup 99
Torsion-free group 21 53 87 99 103 108 110
Totally disconnected 13
Tychonoff theorem 17
Tychonoff topology 17
Uniform space 41
Uniformity 41
Unitary group 2
Unitary matrix 2
Unitary representation 116
Weak direct product 17
Z 1 47 51 55
Z, character group of 47 51
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