Index 831 multiplicity, 415 n-ad, 97 n-connected, 279 map, 279 n-cube diagram, 196 n-equivalence, 277 at P, 443 mod Q, 443 pointwise, 301 n-skeleton, 354 natural, 12 isomorphism, 12 natural grading, 612 natural transformation, 11 of cohomology theories, 462 of represented functors, 12 NDR pair, 104 negative, 506 neighborhood deformation retract, 104 strong, 104 Neisendorfer localization, 786 nerve, 176 Newton polynomial, 697, 807 nilpotency, 555 nonzero, 417 norm, 553 normed algebra, 553 north pole, 46 northern hemisphere, 46 nose on the, 82 nullhomotopic, 82 nullhomotopy, 82 numerable, 309 numerable bundles, 324 objects, 5 obstruction, 360, 642 obstruction theory, 360, 385 odd map, 565 on the nose, 82 open cells, 47 opposite category, 10, 265 opposite-simple category, 169 orbit space, 217 ordinary cohomology theory, 462 ordinary homology theory, 500 existence, 507 orientable, 592 fibration, 203 orthogonal group, 231, 603 over B, 94 p-adic integers, 735 p-completion, 735 P-connectivity, 438, 439 P-group, 438 P-injective, 443 P-local, 730 P-localization, 724 P-surjective, 443 pair, 58, 401, 461 ‘product’, 59 mapping space, 59 pairing, 427 homology with cohomology, 510 parametrized concatenation, 109 partition of unity, 309 path, 70 reverse, 73 path homotopy, 72 path object, 89, 266 standard, 90 path space, 83, 89 perfect, 388 phantom map, 245, 582 existence, 582 nonexistence, 582 πn(Sn), 383 PID, 487, 801 piecewise linear, 75, 297 Poincar´ e series, 574 pointed category, 18 pointed homotopy, 72 pointed map, 60 composition, 20 pointed model category, 263, 264 pointed set, 19, 71 pointed space, 60 pointwise cofibration, 167 pointwise equivalence in hT , 93 pointwise equivalent, 146 pointwise fibration, 147, 270 pointwise homotopy equivalence, 93, 94, 96 in hT , 146 pointwise weak equivalence, 270 polyhedron, 296 polynomial algebra, 793 graded, 796 Pontrjagin algebra, 512 Postnikov approximation, 361 Postnikov section cellular structure, 361 existence, 361 uniqueness, 361 prepullback, 36 prepushout, 37 presentation, 294 prespectra, 580 primitive, 510, 804 principal bundle associated, 335

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