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Eilenberg S., Steenrod N. — Foundations of Algebraic Topology
Eilenberg S., Steenrod N. — Foundations of Algebraic Topology

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Название: Foundations of Algebraic Topology

Авторы: Eilenberg S., Steenrod N.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1952

Количество страниц: 328

Добавлена в каталог: 01.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abstract, category      108
Abstract, cell complex      156
Acyclic, carrier      171
Acyclic,complex      170
Additive functor      121
Adjusted homology sequence      245
Admissible, category      5
Admissible, map      306
Algebraic, homotopy      170
Algebraic, map      170
Alternating chain complex      174
Associated LC-theory      271
Augmented, complex      169
Augmented, singular complex      190
Automorphism of a simplex      82
Axioms for cohomology      14
Axioms for homology      10
Barycenter      61
Barycentric, coordinates      55
Barycentric, subdivision      61 63 177
Base      133
Base point      17
Betti number      52 138
Bihomomorphism      160
Borsuk's separation criterion      302
Boundary      56 74 90
Boundary of a chain      88
Boundary operator      10
Boundary operator of a couple      127
Boundary operator of a traid      35
Boundary operator of a triple      24
Bounded      269
Brouwer fixed point theorem      301
c-functor      114
C.S.      14
Canonical, base      139
Canonical, imbedding      55
Canonical, map into a nerve      286
Carrier      170 234
Carrier, compact      255
Cartesian product      67 131
Category      109
Category of all pairs      5
Category of compact pairs      5
Category of locally compact pairs      5
Category of triangulable pairs      76
Category with couples      114
Cech homology groups      237
Cech homology groups, system      237
cell      44
Cell, complex      156
Cell, relative      311
Chain      84
Chain, complex      124
Chain, homomorphism      84
Chain, homotopy      129
Circuit      106
Closed, covering      233
Closed, path      313
Closed, sot      4
Closure      4
Coboundary      92
Coboundary of a cochain      90
Coboundary operator      14
Coboundary operator of a triad      37
Coboundary operator of a triple      29
Cochain      86
Cochain, complex      125
Cocycle      92
Coefficient group      17 18
Cofinal      212
Cofinal subsystem      214
Cohomology functor      112
Cohomology group      13
Cohomology group of a chain complex      153
Cohomology group of a complex      92 166
Cohomology group, Cech      237
Cohomology group, singular      188
Cohomology sequence of a, pair      14
Cohomology sequence of a, triad      37
Cohomology sequence of a, triple      29
Cohomology theory      13
Cohomology theory of chain complexes      153
Cohomology theory of complexes      166
Cohomology theory, Cech      237
Cohomology theory, singular      188
Cohomotopy groups      49
Collapsible      18
Compact      4
Compact carriers      255
Compactification      270 277
Complement      74
Completely regular      276
Complex, finite      56
Complex, infinite      74 162
Complex, locally finite      75 183
Component      254
Composition of functions      3
Contiguous      164
continuous      4
Continuous homology theory      260
Contractible to a point      30
Contravariant, $\delta$-functor      116
Contravariant, $\partial$-functor      117
Contravariant, functor      111
Coordinate      131
Countercompact      269
Couple      114 126
Covariant, $\delta$-functor      116
Covariant, $\partial$-functor      115
Covariant, functor      111
Covering      233
Covering of a pair      234
Covering theorem      187
cube      276
CYCLE      90
Cylinder      210
Deformation, chain      129
Deformation, retract      30
Degenerate chain      173
Degree of a map      304 306
Development      288
Diagonal form      139
Diagonal form, map      67
Dimension of a complex      56
Dimension, axiom      12
Direct limit      220
Direct product      131
Direct sum      8 10 32 132
Direct system      212
Direct, couple      126
Direct, homology groups      184
Direct, system of upper sequences      224
Directed set      212
Distance in a simplex      55
Domain      109
Domain of integrity      52
Duality      14
Elementary, chain      163
Elementary, subdivision      74 75
Enlargement      261
EQUIVALENCE      109
Equivariant      73
Equivariant, homology groups      209
Essential      299
Euclidean complex and simplex      73
Euler characteristic      53
Exact sequence of groups      8
Exactness axiom      11
Exactness axiom, partial      253
Excision axiom      11 12
Excision map      12 130
Excision map for complexes      165
Excision map, generalized      117
Excisions of various types      267
Ext      161
Face of a singular simplex      186
Face sequence      9
Face, factor, complex      125
Face, of a simplex      55
Finite cochains      183
Five lemma      16
Fixed point theorem      301
Formal homology theory      166
Free, base      133
Free, module      134
Full, subcategory      110
Full, subcomplex      70
functor      111
Fundamental theorem of algebra      307
Generalized excision      117
Generate      133
Grating      254
Group      6
Group of homomorphisms      147
Group of operators      73
h-category      117
h-functor      118
H.S.      11
Hausdorff space      4
Hexagonal lemma      38
Homeomorphic      17
Homologically trivial      22
Homology functor      112
Homology group      10
Homology group of a chain complex      125 151
Homology group of a chain mapping      169
Homology group of a complex      90 166
Homology group of a triad      203
Homology group, Cech      237
Homology group, equivariant      209
Homology group, singular      188
Homology sequence of a, pair      11
Homology sequence of a, triad      35
Homology sequence of a, triple      25
Homology theory      10
Homology theory for normal spaces      282
Homology theory, Cech      237
Homology theory, continuous      260
Homology theory, equivariant      209 for
Homology theory, locally compact spaces      271
Homology theory, singular      188
Homomorphism      7
Homomorphism of a sequence of groups      9 15
Homotopic      6
Homotopic, chain maps      129
Homotopy      6
Homotopy axiom      11 12
Homotopy equivalence      29 117
Homotopy groups      48 207
Homotopy, inverse      117
Horn      147 152
Identity      108
identity map      3
Image      7 9
Imbedding      61
In variance, of dimension      302
In variance, of domain      303
Incidence isomorphism      79 80
Incidence isomorphism, number      156
Inclusion map      3
INDEX      169
Index of a singular chain      190
Indexed family of sets      233
Induced homomorphism      10 14 239
Inessential      299
Infinite, complex      74
Infinite, triangulation      75
Infinitely divisible      159
Injection      8 132 214
Injective representation      8 133
Interior      4
Intersection of a nested system      260
INV      258
Invariance      180
Invariant      73
Invariant under relative homeomorphisms      266
Inverse homology group      184
Inverse limit      215
Inverse system      213
Inverse system of factor groups      228
Inverse system of lower sequences      224
Inverse system of subgroups      228
Isomorphism      7 9
Join      74 172 192
Kernel      7 9
Lattice of a pair      4
LC-theory      271
Lebesgue number      65
Line segment      72
Linear      6
Linear imbedding      61
Linear independence      52 72 133
Linear map      57 60
Linear metric      61
Linear singular simplex      192
Linear subspace      6
Locally Euclidean      303
Locally finite complex      75 183
Lower cap      44
Lower sequence of groups      8
Main isomorphism      94
Manifold      311
MAP      3
Map defined by a map      3
Map, linear      57 60
Map, simplicial      58 60
Mapping cylinder      210
Mappings      109
Maps of inverse and direct systems      213
Mayer homology groups      182
Mayer — Vietoris, formula      53
Mayer — Vietoris, sequence      37 39 42 43
mesh      60
Mesh of a covering      251
Metric topology      75
Module over a ring      6
Monomial      308
Multiplicative system      108
Natural, equivalence      112
Natural, homomorphism      7 10
Natural, transformation      112
Nerve      234
Nested system      260
Nonorien table      313
Nonorien table, circuit      106
Norm      44
Normal pair      278
Normal space homology theory      282
Objects      109
Onto      7 9
Open covering      233
Open set      4
Open simplex      56
Open star      57
Operator group      73
Ordered, chain complex      163
Ordered, complex      67
Ordered, simplex      55
Orientable      313
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