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van der Dries L. — Tame topology and O-minimal structures
van der Dries L. — Tame topology and O-minimal structures



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Название: Tame topology and O-minimal structures

Автор: van der Dries L.

Аннотация:

Following their introduction in the early 1980s, o-minimal structures have provided an elegant and surprisingly efficient generalization of semialgebraic and subanalytic geometry. This book gives a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. It starts with an introduction and overview of the subject. Later chapters cover the monotonicity theorem, cell decomposition, and the Euler characteristic in the o-minimal setting and show how these notions are easier to handle than in ordinary topology. The remarkable combinatorial property of o-minimal structures, the Vapnik-Chervonenkis property, is also covered. This book should be of interest to model theorists, analytic geometers and topologists.


Язык: en

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 180

Добавлена в каталог: 17.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^k$-cell      116
$C^k$-cell decomposition      116
$C^k$-map      116
$C^l$-cell      114
$C^l$-cell decomposition      115
$C^l$-map      111 114
Additive complexity      151 152
Affine coordinates      120
Affine definable space      157
Affine function      26
Affine independent      119
Affine map      126
Affine span      119
Affine subspace      119
Artin, E.      8 21
Aschenbrenner, M.      vii
Asymptotic direction      118
atom      12
Attaching      165
Barycenter      120
Barycentric coordinates      120
Barycentric subdivision      123 129
Basic function      21
Basic relation      21
Basic semilinear set      26
Benedetti, R.      vii 7 8 41 141 150—152 154
Bierstone, E.      8
Bochnak, J.      8 41 106
Boolean algebra      2 12
Borel set      1 16
Boundary      x 18
Bounded      95
Bourbaki, N.      106
box      17
Brown, A.      8 41 118
Brumfiel, G.      8 106 118 155 168
Cantor set      1
Cantor space      1
Cantor's paradise      1
Caratheodory, C.      126
cell      3 50 51
Cell decomposition theorem      4 49—57
Chart      156
Chevalley's constructibility theorem      13 34 76
Closed complex      121
Closed multivalued function      128
Closure      x 2 15 17
Codomain      ix
Compatible      ix 127
Completable      102 159
Completion      163
COMPLEX      121
Cone      149
Conjunction      11
Constant      21
Constant symbol      22
Constructible set      13 76
Continuity of roots      32
Convex      17 120
Convex hull      120
Conway's field of surreal numbers      8
Curve selection      93 94 97
Decomposition      51 52
Decomposition above      38
Decreasing      16
Definable additive map      28
Definable atlas      156
Definable choice      94
Definable collection      5
Definable connected component      57
Definable connected set      19 51
Definable contractible      134
Definable contraction      134 135
Definable curve      102 159
Definable equivalence relation      94 97
Definable equivalent sets      7 132
Definable family      5 59
Definable function      3 19 156
Definable homeomorphic sets      133
Definable homeomorphism type      133
Definable homotopy      134
Definable identifying map      104
Definable map      3 18 22 158
Definable partition of unity      102
Definable path      100
Definable point      22
Definable proper map      104
Definable proper over      166
Definable proper quotient      162
Definable quotient      161—168
Definable retraction      135
Definable set      3 18 22 43 156
Definable set of representatives      94 106
Definable Skolem functions      94 106
Definable space      155—161 168
Definable strong deformation retraction      135
Definable subspace      158
Definable trivialization      142 147
Definable using constants      22
Definable using parameters      22
Definably trivial map      7 142
Definably trivial over      142 147
Delfs, H.      7 8 106 138 154 168
Delzell, C.      41 106
Denef, J.      8 77
Dense      17
Dependency index      83
Dependent      82 84
Derivative      12 107 108
Descriptive set theory      16
Dieudonne, J.      138
Differentiable      107 108
DIMENSION      5 63—69
Disjoint sum      164
Disjunction      11
Division ring      20 28
Domain      ix
Dudley, R.      84 91
Efroymson, G.      8 41 173
Embedded definable homeomorphism type      149
Embedded homeomorphism type      149
Equivalence of definable atlases      156
Esquisse d'un Programme      vii 8 9
Euler characteristic      5 69—76
Existential quantification      11
expansion      23
Extreme point      120
Face      120 128
Family      ix 5
Fewnomial      150
Fiber      59
Fiber wise properties      98
Finiteness lemma      46—49
Finkler, J.      vii
Fixed point theorem      97
Flag      123
Formula      11
Fourier — Motzkin elimination      29
Frontier      x 66
Fuchs, L.      27 29
Full multivalued function      128
Function      ix
Function symbol      22
Gabrielov, A.      8
Generic triviality      148
Giesecke, B.      138
Gluing      156 168
Good direction      6 117 131 142
Graph      ix
Grothendieck, A.      vii 8 9
Hardt, R.      141 154
Hausdorff space      x 95 106 159
Henson, C.W.      vii
Hironaka, H.      8 138
Holly, J.      vii
Implicit function theorem      113
Increasing      16
Independent      82 84
Interior      x 2 17
Interpretation      22
interval      2 17
Interval topology      17
Inverse function theorem      112
Iovino, J.      vii
Jacobian matrix      108
Kechris, A.      16
Keisler, H.      8 29
Khovanskii, A.      9 77 141 168
Knebusch, M.      7 8 106 138 139 154 168
Knight, J.      61
Koopman, B.      8 41 118
Kreisel, G.      vii
l'Hopital's rule      114
L-structure      22
Language      22 23
Laskowski, C.      85 91
Lewenberg, A.      vii
Lifting of a triangulation      129
LIMIT      x 15 46
Line      119
Local dimension      69
Locally bounded      97
Locally closed      51
Lojasiewicz property      37
Lojasiewicz, S.      8 31 33 34 41 138
Macintyre, A.      vii 9 91
MacPherson, R.      8
MAP      ix
Marker, D.      vii p
Matyasevich’s theorem      16
Miller, C.      vii 8 9 41
Milman, P.      8 173
Model completeness      13
Model-theoretic structure      21
Monotone      16
Monotonicity theorem      3 43—46
Morphism of definable spaces      157
Multivalued function      128
Negation      11
Nesin, A.      vii
No ether normalization      6 39 138
o-minimal structure      2 6 16 17 23
Open cell      50
Ordered division ring      27 28
Ordered F-linear space      25
Ordered field      21
Ordered field of real numbers      37
Ordered group      19
Ordered ring      20
Partition      ix 51 52
Peterzil, Y.      3 106
Pfaffian functions      9
Pillay, A.      vii 8 29 61 77 91 168
Plane      119
Poincare, H.      1
Polyhedron      121 170
Polynomially bounded      41
primitive      21
PRODUCT      158
Projective space      157
Proper map      106
Pukhlikov, A.      77
Quantifier elimination      13 29
Ramsey's theorem      86
Real closed field      7 21 76
Real closure      8
refinement      ix
Regular space      158
Relation symbol      22
Restriction      ix 15
Ring      viii 15
Risler, J.-J.      vii 7 8 41 141 150—152 154
Robson, R.      155 159 168
Roy, M.-F.      8 41 106
Schanuel, S.      vii 77
Schreier, O.      8 21
Scowcroft, P.      106
Semialgebraic cell decomposition      33 35
Semialgebraic map      40
Semialgebraic set      1 2 24 31—41
Semianalytic set      8
Semilinear map      119
Semilinear set      1 2 25 26
Sheaf      15 156
Shelah, S.      79 85 91
Shiota, M.      9 154
Sign condition      32
Simple function      24
Simple set      24
simplex      119
Sontag, E.      29 91
Speissegger, P.      vii 106
Star      135
Starchenko, S.      8 29
Steinhorn, C.      vii 8 29 61 91 106
Stengle, G.      91
Stratification      68
Strebonski, A.      77
Strictly decreasing      16
Strictly increasing      16
Strictly monotone      16
Structure      13
Subanalytic set      2 8
Subcomplex      121
Sussmann, H.      8 118 138
Swierczkowski, S.      vii
Tame topology      8 9
Tarski — Seidenberg theorem      2 31 37 41
Tarski, A.      8 21
Taylor's formula      114
Teissier, B.      9
Thom's lemma      31
Thom's lemma with parameters      38
Tietze extension lemma      7 138
Triangulation      127
Triangulation set      127
Triangulation theorem      7 122 130
Trivial map      141
Trivialization theorem      7 147
Underlying set      21
Uniform continuity      97
Uniform finiteness property      53
Universal quantification      12
Van den Dries, L.      vii 8 9 61 106
Vapnik — Chervonenkis class      6 81
Vapnik — Chervonenkis index      81
Vapnik — Chervonenkis property      vii 79—91
Vapnik, V.      91
VC-class      6 81
Vertex map      122
Vertices      120
Viro, O.      77
Whitney, H.      41
Wilkie's Theorem      vii 3 7 8 9 37 141 154
Wilkie, A.      vii 2 9 91 150
Woerheide, A.      vii 138
Yukich, J.      91
Zil'ber Principle      29
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