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Morris S. — Pontryagin Duality and the Structure of Locally Compact Abelian Groups
Morris S. — Pontryagin Duality and the Structure of Locally Compact Abelian Groups



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Название: Pontryagin Duality and the Structure of Locally Compact Abelian Groups

Автор: Morris S.

Аннотация:

These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 136

Добавлена в каталог: 20.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$k_\omega$-space      78
$R^n$      24 27—40
$R^n$, closed subgroups of      33
$T_0$-space      6
$T_1$-space      4
$T_2$-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 $R^n \times Z^m \times K$      36 94
Closed subgroups of $R^n$      33
Closed subgroups of $T^n$      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 $R^n$      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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