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Geroch R. — Mathematical physics
Geroch R. — Mathematical physics

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Название: Mathematical physics

Автор: Geroch R.

Аннотация:

Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.


Язык: en

Рубрика: Математика/Математическая Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 358

Добавлена в каталог: 24.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^*$-algebra      290
Abelian group      17
Abelian group, category of      18
Abelian group, free      19
Accumulation point      163
Additive group of integers      16
Additive group of integers, of reals      16
Adjoint of bounded operator      289
Adjoint of operator      329
Algebra, $C^*$      290
Algebra, associative      97
Algebra, category of associative      97
Algebra, category of Lie      105
Algebra, free associative      98
Algebra, Lie      104
Algebra, quotient      102 105
Algebra, universal enveloping      106
Almost everywhere      266
Associative algebra, category of complex      98
Associative algebra, category of real      98
Associative algebra, complex      97
Associative algebra, free      98
Associative algebra, homomorphism of      98
Associative algebra, ideal of      101
Associative algebra, quotient of      102
Associative algebra, real      97
Associative algebra, representation of      125
Associative algebra, subalgebra of      101
Associative algebra, unit of      103
Basis for Hilbert space      283
Basis for vector space      47
Boundary in homology      204
Boundary in topology      140
Bounded above      40
Bounded operator      285
Bounded operator, adjoint of      289
Bounded operator, eigenvalue of      293
Bounded operator, eigenvector of      293
Bounded operator, inverse of      295
Bounded operator, invertible      295
Bounded operator, norm of      286
Bounded operator, regular value of      295
Bounded operator, spectrum of      295
Cantor set      255
Cartesian product      10
Casimir subalgebra      109 ’
Category      3
Category, composition in      3
Category, direct product      8
Category, direct sum      8
Category, epimorphism      4
Category, identity morphism      3
Category, isomorphism      7
Category, monomorphism      4
Category, morphism      3
Category, object      3
Category, of abelian groups      18
Category, of complete topological groups      237
Category, of complete topological vector spaces      244
Category, of complete uniform spaces      227
Category, of complex associative algebras      98
Category, of complex Lie algebras      105
Category, of complex vector spaces      45
Category, of groups      18
Category, of Hausdorff topological spaces      154
Category, of real associative algebras      98
Category, of real Lie algebras      105
Category, of real vector spaces      45
Category, of sets      4
Category, of topological groups      236
Category, of topological spaces      154
Category, of topological vector spaces      244
Category, of uniform spaces      223
Category, subobject      7
Cauchy net      225
Cauchy sequence      225
Center, of a group      31
Closed operator      340
Closed set      138
Closure      140
Coarser topology      142
Cohomology group      216
Commutator subgroup      30
Commute (diagram)      8
Compact      165 167
Compact, locally      171
Compact-open topology      172
Complement, of a set      134
Complementary subspace      54
Complete topological group      237
Complete topological group, category of      234
Complete topological vector space      244
Complete topological vector space, category of      244
Complete uniform space      225
Complete uniform space, category of      227
Completion of a topological group      237
Completion of a topological vector space      244
Completion of a uniform space      277
Complex associative algebra      97
Complex associative algebra, category of      98
Complex Lie algebra      104
Complex Lie algebra, category of      105
Complex vector space      44
Complex vector space, category of      45
Component      180
Composition of functors      94
Composition of mappings      4
Composition of morphisms      3
Configuration operator      332
Connected      177 178
Connected component      180
continuous      147
Continuous, homomorphism      236
Continuous, linear mapping      244
Continuous, uniformly      222
Continuous, upper semi-      314
Contractible      198
Contravariant functor      92
Converge      161
Converge in measure      269
Convex      246
Convex, locally      246
Coset in group      26
Coset in vector space      54
Countable      7
Covariant functor      90
Covering      165
Curve      195
CYCLE      206
Dense      326
Derivative, of a distribution      273
Diagonal      217
Diagram      8
Diagram, commutative      8
Dimension, of vector space      51
Dirac delta distribution      271
Direct product      8
Direct product, of groups      35
Direct product, of representations      121
Direct product, of sets      10
Direct product, of topological groups      239
Direct product, of topological spaces      155
Direct product, of uniform spaces      224
Direct product, of vector spaces      59
Direct sum      8
Direct sum, of abelian groups      36
Direct sum, of Hilbert spaces      284
Direct sum, of representations      121
Direct sum, of sets      11
Direct sum, of topological groups      238
Direct sum, of topological spaces      157
Direct sum, of topological vector spaces      246
Direct sum, of uniform spaces      224
Direct sum, of vector spaces      59
Directed set      160
Discrete topology      136
Disjoint union of measure spaces      257
Disjoint union of sets      11
distribution      271
Distribution, derivative of      273
Distribution, Dirac delta      271
Distribution, order of      274
Distribution, product of      273
Distribution, sum of      272
Distribution, support of      274
Domain, of an operator      325
Dual, of a vector space      65
Eigenvalue      293
Eigenvector      293
Empty set      134
Entourage      217
Enveloping algebra, universal      106
Epimorphism      5
Equivalence, class      39
Equivalence, relation      39
Equivalence, relation generated by      39
Euclidean topology      242
Extended reals ($R^*$)      249
Extension, of an operator      325
Faithful representation      124
Finer topology      142
First homotopy group      194
Free Abelian group      22
Free associative algebra      98
Free group      19
Free Hilbert space      284
Free object      94
Free topological space      154
Free vector space      45
Function, integrable      263 264
Function, integrable step      262
Function, measurable      259
Function, step      260
Function, support of      270
Function, upper semicontinuous      314
Functor, composition of      94
Functor, contravariant      92
Functor, covariant      90
Functor, forgetful      91
Functor, homology      216
Generated equivalence relation      39
Generated ideal      101 105
Generated normal subgroup      29
Generated subalgebra      101 105
Generated subgroup      25
Generated subspace, of a Hilbert space      281
Generated subspace, of vector space      53
Generated topology      143
Group      16
Group, abelian      17
Group, algebra      98
Group, category of      18
Group, category of abelian      18
Group, category of complete topological      237
Group, category of topological      236
Group, center of      31
Group, cohomology      216
Group, commutator sub-      30
Group, complete topological      237
Group, coset      26
Group, first homotopy      194
Group, free      19
Group, free abelian      22
Group, homology      208
Group, homomorphism of      17
Group, identity      16
Group, inner isomorphism      33
Group, inverse      16
Group, normal sub-      29
Group, of integers      16
Group, of reals      16
Group, permutation      17
Group, quotient      30
Group, representation of      125
Group, sub-      18
Group, topological      234
Group, topological, of reals      235
Hausdorff topological space      144
Hausdorff topological space, category of      154
Hermitian operator      290
Hermitian operator, spectral family of      319
Hilbert space      277
Hilbert space, bounded operator      285
Hilbert space, free      284
Hilbert space, generated subspace      281
Hilbert space, inner product      277
Hilbert space, operator      325
Hilbert space, orthonormal basis      283
Hilbert space, subspace of      280
Homologous      207
Homomorphism, continuous      236
Homomorphism, image      33
Homomorphism, kernel      33
Homomorphism, of associative algebras      98
Homomorphism, of groups      17
Homomorphism, of Lie algebras      104
Homotopic      189
Homotopy      190
Homotopy, group      194
Ideal, generated      101 105
Ideal, of associative algebra      101
Ideal, of Lie algebra      105
Identity, in group      16
Identity, morphism      3
Image of homomorphism      33
Image of linear mapping      58
Image of mapping      134
Indiscrete topology      136
Induced topology      150 151
Infinite-dimensional vector space      51
Inner isomorphism      33
Inner product      277
Integers, additive group of      16
Integrable function      263 264
Integrable step function      262
Integral of function      264
Integral of step function      262
Interior      140
Invariant subobject      122
Inverse, image of mapping      134
Inverse, in group      16
Inverse, of bounded operator      295
Invertible operator      295
Irreducible representation      128
Isomorphism      7
Isomorphism, inner, of group      33
Isomorphism, of Hilbert spaces      284
Isomorphism, of topological spaces      154
Jacobi relation      104
Kernel of homomorphism      32
Kernel of linear mapping      58
Lebesque measure      253
Left coset      26
Lie algebra      104
Lie algebra, Casimir subalgebra      109
Lie algebra, category of complex      105
Lie algebra, category of real      105
Lie algebra, complex      104
Lie algebra, homomorphism of      104
Lie algebra, ideal of      105
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