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| Massey W.S. — Algebraic Topology: an introduction |
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| Предметный указатель |
ARC 56
Automorphisms of a covering space 159 162—163
Ball, n-dimensional xi
Barycentric subdivision 40
Basis for a free group 105
Bordered surface 36—44
Borsuk — Ulam theorem 170—172
Boy, W. 52
Brahana, H.R. 53
Brouwer fixed-point theorem 74
Classification of compact bordered surfaces 37—42
Classification theorem for compact surfaces 10—11 18—29
Classification theorem for noncompact surfaces 50—51
Closed map 245
Cohomology groups 237—240 241—242
Commutative diagram ix—x
Commutator 104
Compactification of a surface 49—50
Connected sum 8—10 51
Connectivity, arcwise or pathwise 56
Connectivity, local arcwise 56
Connectivity, semilocal simple 174
Connectivity, simple 66
Contractible space 66
Convex set 67
Covering spaces 145—188
Covering spaces of a CW-complex 217
Covering spaces of a graph 201
Covering spaces of a topological group 157—158 164
Covering spaces, existence theorem for 173—175
Covering spaces, induced over a subspace 150 177
Covering transformation 159
Crowell, R.H. 141
CW-complex 215—217
Decomposition space 244
Deformation retract 66
Degree of a closed path 70—74
Direct product 85—86
Disc, n-dimensional xi
Double coset 220
Edgepath 193
Elementary neighborhood 146
Endpoint compactification 49
Epimorphism ix
Equivariant map 255—256
Euler characteristic of a bordered surface 42
Euler characteristic of a graph 200
Euler characteristic of a surface 29—33
Fibre bundles 187
Fibre spaces 187
Fox, R.H. 141 186
Free Abelian group 89—97
Free group 102—105
Free group, subgroup of 203—207
Free product of groups 97—100 218—233
Free product of groups, subgroup of 218—224
Free product of groups, with amalgamated subgroups 142
Fundamental domain 185
Fundamental group 55—83 113—141
Fundamental group of a circle 68
Fundamental group of a compact 4-manifold 143
Fundamental group of a compact bordered surface 135 199
Fundamental group of a compact surface 129—135
Fundamental group of a connected sum of manifolds 127
Fundamental group of a covering space 154
Fundamental group of a CW-complex 217
Fundamental group of a figure "8" curve 123—124
Fundamental group of a graph 197—198
Fundamental group of a noncompact surface 143 200
Fundamental group of a product space 76
Fundamental group of a punctured disc or plane 124—125
Fundamental group of a topological group 78
Fundamental group of a union of circles 125
Fundamental group of real projective n-space 166
Fundamental group of the complement of a knot 136—141
Fundamental group, definition 62
Generators for a group 89
Genus of a bordered surface 43
Genus of a surface 33
Graph 190
Group of a knot 137
Group of operators 254
Grushko's theorem 225 235
Hirsch, M. 51
Homogeneous space 256
Homogeneous space, automorphism group 257—258
Homology groups 237—240 241—242
Homomorphism of covering spaces 158
Homomorphism, induced by a continuous map 63 237 238
Homotopic maps 64
Homotopy 64
Homotopy equivalence 82
Homotopy groups 236—237
Homotopy groups of a covering space 187—188
Homotopy type 82
Homotopy type vs. topological type 142
| Hurewicz, W. 83 236 237
Ideal boundary 49
Identification topology 243—253
Immersion 52
Inclusion map x
Induced homomorphism 63 237 238
Isomorphism (of groups) ix
Isotropy subgroup 256
Kerekjarto, B. 50
Kervaire, M. 241
Klein bottle 9
Knot 136
Kuratowski's theorem 208
Kurosh subgroup theorem 218—220 234—235
Lebesgue number 69
Lifting of maps 155—156
Lifting of paths 151—152
Local arcwise connectivity 56
Local homeomorphism 149—150
Loop 62
Manifold 240—241
Manifold with boundary 35—36
Manifold, definition 2
Manifold, orientable vs. nonorientable 3—6
Markov, A.A. 53 144
Milnor, J. 241
Moebius strip 3—4
Moise, E. 52
Monomorphism ix
n-dimensional manifold 2
n-dimensional manifold with boundary 35—36
Nielsen, J. 208
Normalizer of a subgroup 257—258
Number of sheets of a covering space 154 162
Open map 245
Orbit 244
Paths 56
Paths, closed 62
Paths, equivalence of 56—57
Paths, product of 57—58
Permutation groups 254—258
Poincare conjecture 142 241
Poincare group 62
Poincare, H. 83 142 237
Presentation of a group 105—108
Principle, semi-mystical 158
Product of groups, direct 85—86
Product of groups, free 97—100
Product of groups, weak 86—87
Product of sets x
Projection 146
Projective plane 7—8
Properly discontinuous group of homeomorphisms 165 167—170
Pruefer surface 47
Quotient topology 243—253
Rado, T. 16 47 52
Rank of a free abelian group 95
Rank of a free group 105
Reduced word 104
Regular covering space 163
Reidemeister, K. 208
Restriction of a map x
retract 65
Richards, I. 50
Schreier system 205
Schreier, O. 140 208
Seifert, H. 141
Seifert, H., theorem of 113—116
Sheets of a covering space 154 162
Smale, S. 142
Sphere, n-dimensional xi
Stallings, J. 225 235
Subdivision of a graph 191
surface 6
Surface, bordered 36—44
Surface, noncompact 47—51
Symmetric group 254
Topological type xi
Torsion, coefficients 96
Torsion, subgroup 96
Torus 6—7
Torus Knot 137
Transformation groups 254—258
TREE 194
Tree, maximal 196
Triangulation of a bordered surface 38—39
Triangulation of a compact surface 16—18
Triangulation of a noncompact surface 47
Triangulation of manifolds 52 240—241
Universal covering space 160
Universal mapping problems 108—110
Van der Waerden, B.L. 110
Van Kampen's theorem 113—116
van Kampen, E.R. 141
Weak product of groups 86—87
Weak topology 190 198 215
Whitehead, J.H.C. 51 209 211 234
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