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| Geroch R. — Mathematical physics |
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| Предметный указатель |
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, associative 97
Algebra, C*- 290
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
C*-algebra 290
Cantor set 255
Cartesian product 10
Casimir subalgebra 109
Category 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, 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, 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, category of 244
Complete topological vector, space 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 of integers 16
Group of reals 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, 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 of associative algebras 98
Homomorphism of groups 17
Homomorphism of Lie algebras 104
Homomorphism, continuous 236
Homomorphism, image 33
Homomorphism, kernel 33
Homotopic 189
Homotopy 190
Homotopy, group 194
Ideal of associative algebra 101
Ideal of Lie algebra 105
Ideal, generated 101 105
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 in group 16
Inverse of bounded operator 295
Inverse, image of mapping 134
Invertible operator 295
Irreducible representation 128
Isomorphism 7
Isomorphism of Hilbert spaces 284
Isomorphism of topological spaces 154
Isomorphism, inner, of group 33
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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