Index absolute neighborhood retract, 12 retract, 12 self-intersector, 182 abstract regular neighborhood, 213, 219 acyclic, 17 Alexander 3-cell, 49 Cantor set, 51, 52 horned sphere, 47, 50 invariant, 274 isotopy, 202 matrix, 305 polynomial, 301 Alexander-Newman Theorem, 27 Alexandroff Theorem, 14 Alford arc, 89 sphere, 88 algebraic unknotting, 279, 295 α-equivalence, 427 ambient dimension, xvi space, xiv Annulus Theorem, 65, 374 ANR, 12 antipodal map, 183 points, 183 Antoine 3-cell, 46, 171 Cantor set, 46 necklace, 42, 125, 169, 172, 175 sphere, 46 Approximation Problem, xvi Approximation Theorems, 162, 227, 243, 263, 325, 347, 366, 370, 382, 384, 398, 403, 438, 440 AR, 12 ball, xiv β-map, 427 β-statement, 168 bicollar, 62, 356 pinched, 93 binary icosahedral group, 18, 281 Bing dogbone space, 60 hooked rug, 83 house with two rooms, 189 shrinking criterion, 56 sling, 80, 424 Blankinship Cantor set, 169, 172, 175 Borel Conjecture, 442 Borromean rings, 311 boundary manifold (∂-manifold), 2 of a ∂-manifold, 2 operator for homotopy groups, 11 ∂-manifold, 2 bouquet of circles, 1 branching system, 236, 388 Bryant-Seebeck engulfing, 115, 127 Bubble Lemma, 377, 382 Cantor set, 42 cell, xiv with holes, 374 cell-like embedding relation, 383 mapping, 109 463
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