Valentine F.A. — Convex Sets :: Электронная библиотека попечительского совета мехмата МГУ

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Valentine F.A. — Convex Sets

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Название: Convex Sets

Автор: Valentine F.A.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 246

Добавлена в каталог: 27.03.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

intersection property      79
$(\mathcal{R},E)$       61
$A\times B$       198
      156
-convex set      50
      36
$H_{j}$       107
$H_{u}$       59
-dimensional section      91
-point simplicial property      42
$K(a,\rho)$       34
-partitionable property      79
      31
$P_{3}$       114
-convex      99
-convex hull      99
      54
$S^{*}$       120
$T_{0}$ space      164
$T_{1}$ space      200
$V_{i}$       105
      157
$W_{ij}$       105
-star      93 174
$x\cdot y$       57 208
      99
$\beta$ -cone      136
Absolute value      197
Additive functional      21
Affine Helly property      177
All-sided family      40
ARC      105
Area      144
Auswahlsatz      37
Ball      34 205
Banach space      203
Basis for $\mathcal{L}$       7
Basis for topology      198
Bilinear functional      202
Blaschke convergence theorem      37
Body, convex      13 94
Body, parallel convex      34 154
Body, rough convex      134
Body, smooth convex      94 134
Body, strictly convex      94
Boundary of set      5 196 199
Bounded set      33
box      37 208
Breadth      156
Brunn — Minkowski theorem      190
Cartesian product      198
Cauchy condition      40 202
Cauchy sequence      202
Cauchy’s formula for surface area      187
Centrally symmetric neighborhood      6
Centroid      189
Chebyshev set      179
Circles and spheres      190
Closed convex hull      13
Closed set      199
Closed subset      199
Closure of set      5 196 199
Common transversals      79
Compact family      93 148
Compact set      199
Complement of set      196 199
Complementary sets      19
Complete inner-product space      208
Complete set of constant width      159
Complete space      40 203
Component of set      201
Concave functional      134
Cone of support      135
Conjugate space      203
Constant breadth      158
Continuous function      200
Continuum      91
Convergence of sequences      200
Convex arc      105
Convex body      13 94
Convex circular polygon      101
Convex cone      27
Convex cone, vertex of      27
Convex connectedness      169
Convex curve      105
Convex function      27—28 129
Convex functional      27—28 129 233
Convex hull      13—17 39—42 196
Convex kernel      5
Convex polyhedron      141
Convex set      4
Convex subset of spherical surface      175
Convexly arcwise connected set      112
Core of set      11 196
Core point      11
Core topology      165
Countably compact      200
Covering of set      199
Crosscut      48 201
Cylinder      122
Decomposition of a space      119
Decomposition space      120
Deficiency      19
Dense set      120
Diameter       100
Diameter of set      100
DIMENSION      25
Dimension of convex set      7
Distance of from       35
Double-isosceles three-point property      182
Dual cone      61
Dually similar convex sets      66
Emergency axiom      198 (see also Warning)
Empty set      195 (see also Warning)
Encompass      40
Equichordal point      191
Equichordal problem      192
Euclidean space      7 57 208
Exercise, definition of      163
Exp       139
Exposed point      52
Ext       139
Extended support function of convex set      58
Exterior normal ray      135
Extremal ray      186
Extremal subset      137
Extreme point      137
Family, compact      93 148
Family, irreducible      40
Family, uniformly bounded      37
Farthest point mapping      98
Finite intersection property      200
First category      121
Fixed point      207
Flat      7
Flat, dimension of      7
Flat, of deficiency       19
Frechet differentiable      184
Function      200
Function, continuous      200
Function, graph of      130 200
Function, notation for      197
Functional      21 27
Functional notation      197
Functional, additive      21
Functional, bilinear      202
Functional, concave      134
Functional, convex      27—28 129
Functional, homogeneous      21
Functional, linear      21

Functional, locally supported      132
Functional, Minkowski distance      31
Functional, subadditive      60
Functional, support      60
Gateaux differential      132
Generalized continuum      91 202
Generalized ellipses      185
Graph of function      130 200
Hahn — Banach theorem      28
Half-cell of support      55
Half-line      27
Half-spaces      23
Hausdorff linear space      see Topological linear space
Hausdorff space      3 199
Helly’s theorem      70
Heroic principle      185
Hilbert space      45
Homeomorphic image      201
Homeomorphism      201
Homogeneous functional      21
Hull, -convex      99
Hull, closed convex      13
Hull, convex      13—17 39—42 196
Hyperplane      19 197
Hyperplane of support      27
Hyperplane, bounding      23
Hyperplane, properly separating      23
Hyperplane, separating      23
Hyperplane, strictly separating      23
Hyperplane, supporting      27
Identity ( $\equiv$ )      196
Identity of real field      3
If and only if      198
INDEX      237
Induced topology      120
inf      197
Inner product      57
Integral theorems      154 187—188
Interior of set      5 196 199
inversion      110
Irreducible family      40
Isoperimetric inequality      188
Isoperimetric problem      149 152
Jordan curve      201
Kerneigebiet      5 (see also Convex kernel)
Kernel      5
Krasnosel’ski $\breve{\imath}}$ ’s theorem      82—86
Lattice      205
Limit inferior      39
Limit point      199
Limit superior      39
Lin       11 196
Lina       11
Line      7
Line segment      4 196
Linear combination of convex sets      153
Linear functional      21
Linear programming      207
Linear space      3 195
Linear space, axioms for      3
Linear variety      see Flat
Linearly accessible point      11
Linearly bounded set      31
Linearly dependent set of points      7
Linearly independent set of points      7
Linearly isomorphic space      7
Linearly ordered set      205
Lipschitz condition      168
Locally -convex set      51
Locally compact space      199
Locally connected set      202
Locally convex space      26
Locally polyhedral set      141
Locally star-shaped space      6
Locally supported functional      132
Locally symmetric space      6
Manifold      115
Mapping      200
Mapping, into mapping      200
Mapping, onto mapping      200
Maximal convex subset      117
Maximal element      205
Maximal subset      7 205
Metric      33
Metric space      206
Mild convexity      53
Mild local nonconvexity      49
Mildly locally -convex set      51
Minimal covering      37
Minimal element      205
Minimax theorem      206
Minkowski distance functional      31
Minkowski space      34
Motzkin set      179
Motzkin’s theorem      94
Neighborhood of a point      199
Nondegenerate continuum      121
Norm      33 197
Normable topological linear space      33
Normal cone      135
Normally convex set      176
Normed linear space      34
Nowhere dense set      121
Origin      3 195
Orthonormal basis      208
Parallel body      34 154
Parallel element      123
Parallel flats      7
Parallel set      34
Parallelepiped      208
Partially ordered set      205
Piercing cylinder      123
Plane section      91
Plank problem      193
Point(s), can see       86
Point(s), can see       83
Point(s), core      11
Point(s), equichordal      191
Point(s), exposed      52
Point(s), extreme      137
Point(s), fixed      207
Point(s), limit      199
Point(s), linearly accessible      11
Point(s), linearly dependent set of      7
Point(s), linearly independent set of      7
Point(s), neighborhood of      199
Point(s), regular      83
Polar cone      135
Polyhedral set, locally      141
Problem, definition of      163
Product space      28 198
Projective space      192
Projective space, convex sets in      192
Proposition, definition of      163
Radius of support      54
Ray      27
Real field      3 195
Real inner product      57
Rectifiable curve      148
Reflexive      204
Regular point      83
Regular simplex      193
Regular topological space      206
Relative interior of set      9 196
Relative topology      120
Reuleaux polygon      101
Rext       186
Rough convex body      134
Scalar multiple of set      5 196
Scalar multiplication      3 195

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