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Moise E.E. — Geometric topology in dimensions 2 and 3
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Название: Geometric topology in dimensions 2 and 3Автор: Moise E.E. Аннотация: Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the Schonflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1977Количество страниц: 271Добавлена в каталог: 30.10.2010Операции: Положить на полку |
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Abstract complex 53 Acyclic linear graph 156 Alexander, J.W. 81 117 133 Alphabet 107 Annular strip 157 Annulus (=k-annulus) 91 Approximation (= 46 Approximation (= 46 ARC 4 Arc between P and Q 19 Arcwise accessible 70 Artin, Emil 139 Ball 16 Barycenter 45 Barycentric coordinates in a Euclidean complex 3 7 Barycentric coordinates in a PL complex 54 55 Barycentric subdivision 45 Base point 97 BD 4 Betti group 162 Betti number 162 Bi-collar neighborhood 192 Bijective function 3 Bing, R.H. 252 254 Boundary 4 Brick decomposition 34 Broken line 12 Broken-line-wise connected 12 Brouwer, L.E.J. 5 Canonical homomorphism 99 Cantor set 83 Carries 198 cell 4 Cell-complex 117 Cell-decomposition 118 Cellular homeomorphism 197 Center of a pseudo-cell 223 Circular solid torus 127 Classification of 2-manifolds 155 163 Codomain of a function 3 Collar neighborhood 192 Combinatorial boundary 5 Combinatorial equivalent 4 Combinatorial n-cell 4 Combinatorial n-manifold 5 Combinatorial solid torus (CST) 178 Commutator subgroup 99 100 Complete in the sense of Dedekind 14 COMPLEX 2 Component C(M,P) of a set M 12 Connected complex 9 Connected set 10 Connected space 10 Continuous function 4 Continuum 85 Convex 2 Convex hull 2 Coordinate mapping 54 Covering 174 Covering spaces 174 Crossing word 105 CST 178 Cyclic order on a 1-sphere 23 Cylindrical diagram of a solid torus 179 Dehn lemma 190 199 Dehn, Max 190 Dense in 4 Diagram of a Euclidean complex 52 Diagram of a link 101 Diameter 34 Dimension of an abstract complex 53 Disk 4 Distance function 1 Distance functions 6 Domain of a function 3 Dual cell 223 End-point of a linear graph 73 End-point of an arc 19 Equivalent coverings 180 Euclidean complex 2 Euclidean realization of an abstract complex 54 Euler characteristic 147 Exterior of a connected 2-manifold in 195 Exterior of a polygon in a plane 18 Face 2 Finite polyhedron 3 Finite-dimensional 53 Fox, Ralph H. 139 FR 4 Frame of M 72 93 Free group F(A) with alphabet A 108 Free group on n generators 108 Free simplex 27 121 Frontier 4 Full Klein bottle 179 Function 3 Fundamental group 97 General position 2 Generator of a free group 108 Generator word 104 Graeub, W. 117 Handle 151 154 Harrold, O.G., Jr. 146 Hauptvermutung, for 2-manifolds 64 Hauptvermutung, for 3-manifolds 253 Hausdorff space 6 Homeomorphic 4 Homeomorphism 4 Homogeneous space 83 Homology group 6 Homotopic 81 Homotopy between 81 Hudson, J.F.P. 57 Hyperplane 2 i-skeleton of a Euclidean complex 3 i-skeleton of an abstract complex 53 Imbedding 51 Induced homomorphism 98 176 Injective function 3 Inseparable in M 83 int 4 Interior of a connected 2-manifold in 195 Interior of a manifold with boundary 4 Interior of a polygon in a plane 18 Interior of a set in a topological space 5 Invariance of domain 5 Irreducible continuum between P and Q 89 Isomorphism, between two abstract complexes 53 Isomorphism, between two Euclidean complexes 4 Isotopy 81 Johansson, I. 190 Join of A and 44 Join of A and B 44 Jordan curve theorem 31 k-annulus 91 k-face 2 K-fold covering 177 k-sheeted covering 177 Klein bottle 151 Kline, J.R. 96 Kneser, H. 190 Latitudinal polygon 202 Lens space 211 Linear function 3 Linear graph 22 Linear ordering 14 Linearly accessible from U 29 66 Linearly ordered space 23 Link 5 Link in 101 Locally commutative at P 137 Locally commutative at P, connected 89 Locally commutative at P, simply connected 142 Locally commutative at P, tame 145 254 Loop 182 Loop theorem 183 193 194 Manifold 4 Manifold with boundary 4 Mapping of one set into another 9 Mapping of one space into another 4 Mesh 35 59 Metric space 1 Middle-third Cantor Set 80 Moebius band 151 Moore Kline theorem 96 n-cell 4 n-manifold 4 Neighborhood 1 Neighborhood of a set M 2 Nonsingular 182 Norm 58 Open 2-cell 223 Open cell-complex 147 Open cell-decomposition 147 Order of a vertex 24 Orientable 153 170 Orientation 153 170 Papakyriakopoulos, C.D. 183 190 193 Path 9 Path from P to Q 9 Path in M 9 Pathwise connected 9 Piecewise linear mapping 4 PL 42 PL cell-complex 118 PL complex 56 PL manifold 197 PL Schoenflies theorem 122 PL simplex 55 PLH 42 Poincare conjecture 208 Poincare, Henri 207 Polyhedron 3 Projective plane 152 164 Pseudo-cell 223 Pseudo-manifold 173 Push property 30 118 Refinement of a collection of sets 3 Regular neighborhood 155 Relation 108 retract 39 Retraction 39 Rudin, Mary Ellen 125 Schoenflies theorem 68 71 72 Semi-locally tame 145 254 Separable space 4 Separated sets 10 Separates P from Q 22 Separates two sets from one another in a connected set 22 214 Shalen, Peter B. 218 252 Shapiro, Arnold 190 Simplex in 2 Simplicial mapping, for Euclidean complexes 3 Simplicial mapping, for PL complexes 56 Simply connected 98 Simply imbedded 120 Singular 2-cell 182 Singular 2-cell, with no singularities on its boundary 190 Skew graph of type 1 23 79 Skew graph of type 2 24 79 Solid torus 127 Sphere 16 Spherical shell 215 Splitting disk 223 Splitting operation 150 STABLE homeomorphism 82 Stallings, John 183 190 211 Standard n-ball 16 Standard n-sphere 16 Standard position 202 Star of a set in a collection of sets 89 Star of a vertex in a complex 5 Strip neighborhood 16 Strongly positive 46 Subdivision of a Euclidean complex 3 Subdivision of a PL complex 56 subspace 2 Subspace topology 2 Support 55 Surjective function 3 Tame 72 Tamely imbedded 72 Topological linear graph 22 Topological space 2 Topological tree 24 Topology induced by a neighborhood system 2 Toroidal shell 216 Torsion group 162 Torus 151 Totally disconnected set 83 TREE 24 Trefoil knot 114 Triangulated manifold (or manifold with boundary) 5 Triangulation of a set 16 Tube 223 Twisted strip 157 Two-sided surface 191 Two-sphere, with n cross-caps 152 Two-sphere, with n handles 152 Two-sphere, with n holes 152 Universal covering 175 Unknotted in C 134 Vertex 2 Vertex of order n 24 Whitehead, J.H.C. 190 Wild 72 Wild 2-spheres 132—145 Wild arcs 132—139 Wilder, R.L. 139
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