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Rushing T.B. — Topological Embeddings |
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Предметный указатель |
-Statement 91 221 270
-Push 111
-Push, piecewise linear 111
-Neighborhood 120
-Push 120
-Tame 120
-Statement 262
-Statement 240 241 270
-Statement 263
-Statement 264
1-Short shrink (1-SS) 85
Abelian local fundamental group 221
Admissible polyhedron pair 261
Alexander horned sphere 47 69
Alexander — Newman theorem 48
Alexander, J.W. 30 47 48 69 72 271 296
Alexandroff, P.S. 4 238 296
Alford, W.R. 58 73 84 86 87 296
Allowable embedding 42 241
Ambient isotopy see “Isotopy”
Ambient Space 9
Andrews, J.J. 74 296
Annulus conjecture 50
Antoin's necklace 71
Antoine, M.L. 71 72 296
Approximating embeddings (PL) 249—259
Approximating theorem (PL) 251
ARC 99
Arens, R. 273 296
Armentrout, S. 84 296
Artin, E. 61 68 301
Ball, B.J. 58 296
Barden, D. 208 290 297
Barycenter see “Simplex”
Barycentric coordinates 5
Barycentric subdivision see “Simplicial complex”
Berkowitz, H.W. 250 256 263 297
Bicollar 34 41 see
Bicollar theorem 41
Bing's hooked rug see “Hooked rug”
Bing's house with two rooms see “House with two rooms”
Bing, R.H. 13 16 17 18 69 71 73 74 84 111 118 132 149 184 185 193 214 219 297
Blankenship, W.A. 70 72 84 182 297
Brown, M. 35 47 84 88 108 193 297 298
Bryant, J.L. 84 119 132 134 250 259 260 270 295 298
Burgess, C.E. 74 298
Cannon, J.W. 74 298
Canonical Schoenflies theorem 277
Cantrell, J.C 3 84 85 91 99 100 101 102 133 137 214 221 222 260 269 270 293 298 299
Cellularity criterion 178—183
Cernavskii, A.V. 91 100 105 137 214 221 241 247 250 251 259 271 272 278 283 288 294 295 299
Cobordism 206
Cobordism theorems, H 208
Cobordism theorems, s 208
Cobordism, composed 207
Cobordism, H 206
Cobordism, invertible 207
Cobordism, product 207
Codimension 56
Coelbo, R.P. 72 299
Cohen, M.M. 18 21 48 256 299
Collapse, elementary 16
Collapse, elementary simplicial 15
Collapsible 17
Collapsible, simplicially 15
Collar 33—44
Collar, piecewise linear 156
Collar, pinched 41
Collaring theorems 35 40 41 42 242 247
Combinatorial manifold 10
Combinatorial manifold, boundary of 14
Compact-open topology 272
COMPLEX see “Simplicial complex”
Concordance 177
Concordance theorem 177
Cone 11
Connell, E.H. 185 193 200 208 299
Connelly, R. 42 185 260 295 299
Convex hull 5
Convex set 5
Crowell, R.H. 4 52 299 300
Crushing lemma 246
Curtis, M.L. 74 84 178 296 300
Cylindrical triangulation 188
Dancis, J. 119 132 250 297 300
Daverman, R.J. 91 184 294 300
Debrunner, H. 91 97 300
Decomposition theorems 44 75 84 see
Degenerate map 28
Dense subset of Hom, (X,A;M) 121
Derived neighborhood 20
Derived neighborhood, relative 23
Derived subdivision 6
Derived subdivision, (relative) 256
Direct homomorphism system 60
Direct limit group 60
Directed set 60
Dogbone space 74
Doyle, P.H. 58 91 97 105 137 300
Duvall, P.F., Jr. 184 300
Dyer, E. 271 302
Edwards, C.H. 4 9 84 99 100 133 137 298 300
Edwards, D.R. 185 193 272 278 283 288 290 298
Eilenberg, S. 3 161 183 184 300
Embedded space 9
Embedding 1
Embedding theorems, Irwin's 170
Embedding theorems, Penrose — Whitehead — Zeeman 171 251
Embedding, 1-ALG 221
Embedding, allowable 241
Embedding, equivalent embeddings 2
Embedding, locally flat 33
Embedding, locally homotopically unknotted 221
Embedding, locally nice 182 183
Embedding, locally tame 84 120
Embedding, proper 177
Embedding, wild 51
Engulfing 148—219
Engulfing theorems 106 150 166 169 170 186 187 192 193 200 209 215 219 223 241 see
Equivalent embeddings see “Embedding”
Euclidean half-space 2
Everywhere wild submanifold 85
Expansion Lemma 225
Factorization theorems 75 83 84
Fisher, G.M. 271 300
Flat cell pair 91
Flat embedding 51
Flat pair 137
Flattening theorems 74 270
Flattening theorems, for arcs 99
Flattening theorems, for cells 105 106
Flattening theorems, for codimension one spheres 100 101
Flattening theorems, for codimension one submanifolds 136
Flattening theorems, for half-strings 108 109
Flattening theorems, for sphere pairs 158
Flattening theorems, for strings 110 164
Flores, G. 27 300
Floyd, E.E. 271 300
Fort, M.K., Jr. 71 271 300 30J
Fox, R.H. 52 58 61 68 70 72 91 95 97 271 297 300 301
Free group 53
Full subcomplex 19 244
Fundamental neighborhood sequence 57
Gauld, D. 277 301
General position 26—30
General position theorem 28
General position, ratio changing 115
Gillman, D.S. 87 89 301
Glaser, L.C 4 7 9 16 18 20 26 30 48 58 68 84 158 185 193 300 301
Gluck, H. 118 120 131 193 298 301
| Goodrick, R.E. 18 301
Greathouse, C.A. 119 301
Greenberg, M. 161 301
Gugenheim's unknotting theorem 111
Gugenheim, V.K.A.M., Ill 154 301
h-cobordism 206
h-cobordism theorem 208
Half-string 84 108 109
Hamstrom, M.E. 271 302
Handle straightening lemma 278
Handlebodies 31—33
Handlebody decomposition theorem 31
Handlebody lemma 264
Harley, P.W. 68 84 302
Harrold, O.G., Jr. 58 95 183 221 301 302
Hauptvermutung 293
Hauptvermutung, for open cells 154—157
Hauptvermutung, for PL manifolds 14
Hauptvermutung, for polyhedra 13
Hempel, J.P. 182 184 302
Henderson, D.W. 26 302
Hilton, P.J. 180 302
Hirsch, M.W. 166 290 302
Hocking, J.G. 3 4 16 30 47 58 105 300 302
Homma's approximation technique 253
Homma's trivial range theorem 127
Homma, T. 118 250 251 256 302
Homogeneous space 4
Homotopy (short) 219
Homotopy Extension Theorem 180
Hooked rug 72
Horn 223—224
House with two rooms 15
Hsiang 294 302
Hu, S.-T. 86 139 140 154 162 302
Hudson's concordance theorem 177
Hudson, J.F.P. 4 6 9 20 21 26 154 171 177 302 303
Huebsch, W. 277 303
Hurewicz, W. 26 235 303
Husch, L.S. 21 303
Hutchinson, T. 100 137 303
Hyperplane 4
i-Locally connected space 253
Immersion 276
Immersion lemma 276
Index of handle 32
Inessential subspace 166
Infinite engulfing 214—219 223 241
Infinite piping 218
Infinite polyhedron 9
Invariance of domain theorem 3
Irwin's embedding theorem 170
Irwin, M.C 171 303
Isomorphism 8
Isotopy 2 273
Isotopy, -isotopy 120
Isotopy, ambient 20
Isotopy, invertible 4
Isotopy, isotopically equivalent embeddings 2
Isotopy, piecewise linear 20
Isotopy, proper 177
Isotopy, pseudo-isotopy 76
Join, of complexes 10
Join, of polyhedra 11
Join, of simplexes 10
Jordan curve theorem 47
Jordan — Brouwer separation theorem 47
k-connected manifold 166
Kirby, R.C 50 91 100 136 137 193 200 223 260 272 278 282 283 288 294 295 300 303
Kister, J.M., Ill 118 132 199 271 277 297 303
Klee trick 74—75
Klee, V.L. 74 303
Kneser, H. 271 303
Knot 51
Knot, group of 51
Knotted embedding 51
Kwun, K.W. 84 303
Lacher, R.C 91 102 105 137 138 183 214 221 240 270 298 303 304
Layer homeomorphism 273
Lees, J.A. 200 208 304
Lickorish, W.B.R. 261 304
Linear map, of complexes 8
Linear map, of infinite complexes 9
Linear map, of simplex 5
Link 10
Linked spheres 30 262
Local homotopy groups 56—58
Locally 1-connected (1-LC) 85 183
Locally bicollared 34
Locally collapsible subcomplex 255
Locally collared 34
Locally contractible space 253 274
Locally Euclidean space 3
Locally finite simplicial complex 9
Locally flat embedding 33
Locally homotopically unknotted embedding 221
Locally nice embedding 182 183
Locally nice subpolyhedron 183
Locally p-connected complement 221
Locally tame embedding 84 120
Majorant 272
Majorant topology 272
Manifold, boundary of 3
Manifold, closed 3
Manifold, combinatorial 10
Manifold, interior of 3
Manifold, open 3
Manifold, piecewise linear 9—14
Manifold, topological 2—4
Manifold, unbounded 3
Martin, J.M. 18 304
Mazur, B. 47 84 100 208 304
McMillan, D.R. Jr.
mesh 6
Michael, E.A. 35 304
Mildly wild arc 95
Mildly wild n-frame 95
Miller, R.T. 251 260 294 295 304
Milnor, J. 14 208 304
Moise, E.E. 13 14 154 193 304 305
Monotone union of open n-cells 109
Monotone union of PL n-cells 155
Monotonically r-connected 200
Morse, M. 47 100 277 303 305
n-ball 10
n-cell 2 105 44—50 178
n-Cell, closed 2
n-Cell, open 3
n-Cell,with respect to PL-cells 178
n-Cube (standard) 2
n-frame 95
n-sphere 2
n-Sphere, piecewise linear 10
Natural parameterization 245
Natural parameterization lemma 244
Newman, M.H.A. 48 154 200 208 305
p-connected pair 150
p-connected pair, monotonically 200
Partial order relation 60
Penrose — Whitehead — Zeeman embedding theorem 171 251
Penrose, R. 171 305
Piecewise linear manifold 9—14
Piecewise linear manifold, boundary of 10
Piecewise linear manifold, interior of 10
Piecewise linear map, of complex 8
Piecewise linear map, of infinite complex 9
Piecewise linear map, of infinite polyhedron 9
Piecewise linear map, of polyhedron 8
Piercing segment 71
Pinched collar 41
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