viii Contents
Chapter 2. Wild and Flat Embeddings 41
§2.1. Antoine’s necklace and Alexander’s horned sphere 41
§2.2. Function spaces 53
§2.3. Shrinkable decompositions and the Bing shrinking criterion 55
§2.4. Cellular sets and the Generalized Sch¨ onflies Theorem 59
§2.5. The Klee trick 66
§2.6. The product of
R1
with an arc decomposition 67
§2.7. Everywhere wild cells and spheres 73
§2.8. Miscellaneous examples of wild embeddings 75
§2.9. Embeddings that are piecewise linear modulo one point 91
Chapter 3. Engulfing, Cellularity, and Embedding Dimension 97
§3.1. Engulfing without control 98
§3.2. Application: The cellularity criterion 106
§3.3. Engulfing with control 114
§3.4. Application: Embedding dimension 123
§3.5. Embeddings of Menger continua 130
§3.6. Embedding dimension and Hausdorff dimension 136
Chapter 4. Trivial-range Embeddings 145
§4.1. Unknotting PL embeddings of polyhedra 146
§4.2. Spaces of embeddings and taming of polyhedra 152
§4.3. Taming 1-LCC embeddings of polyhedra 159
§4.4. Unknotting 1-LCC embeddings of compacta 161
§4.5. Chart-by-chart analysis of topological manifolds 162
§4.6. Detecting 1-LCC embeddings 163
§4.7. More wild embeddings 169
§4.8. Even more wild embeddings 172
Chapter 5. Codimension-three Embeddings 181
§5.1. Constructing PL embeddings of polyhedra 182
§5.2. Constructing PL embeddings of manifolds 190
§5.3. Unknotting PL embeddings of manifolds 196
§5.4. Unknotting PL embeddings of polyhedra 211
§5.5. 1-LCC approximation of embeddings of compacta 227
§5.6. PL approximation of embeddings of manifolds 243
§5.7. Taming 1-LCC embeddings of polyhedra 261
§5.8. PL approximation of embeddings of polyhedra 263
Previous Page Next Page