Borchers H.J., Sen R.N. — Mathematical Implications of Einstein-Weyl Causality :: Электронная библиотека попечительского совета мехмата МГУ

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Borchers H.J., Sen R.N. — Mathematical Implications of Einstein-Weyl Causality

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Название: Mathematical Implications of Einstein-Weyl Causality

Авторы: Borchers H.J., Sen R.N.

Аннотация:

The present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The authors propose an axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one that is locally a differentiable manifold. The mathematical level required of the reader is that of the graduate student in mathematical physics.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 191

Добавлена в каталог: 18.06.2008

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Предметный указатель

$\beta$ -boundary of $C^{\pm}_{x}$       27
$\tau$ -interior of      27
Affine      8
Antisymmetric, relation      16
Assumption, dimensionality      80
Assumption, first countability      76
Assumption, local precompactness      72
Assumption, overlapping cover      61
Assumption, total boundedness      72
Axiom, cone      25
Axiom, convexity      34
Axiom, density      17
Axiom, identification      21
Axiom, local structure      45
Axiom, order      17
Bundle, coordinate transformations on      169
Bundle, fibre      169
Bundle, reduction of the group      171
Bundle, tangent      171
Cardinal, nonmeasurable      165
Causality      4 5
Completeness, for uniform spaces      68
Completion, order      73
Condition, local triviality      170
Cone      23
Cone, backward      23
Cone, double      2 5
Cone, forward      23
Cone, future      23
Cone, local      74
Cone, past      23
Continuity, uniform      162
Coordinates, cylindrical, on D-intervals      114—115
Coordinates, radar      144
Curve, spacelike      109
Curve, timelike      103
Cushion      129
Cushion, problem      129
D-interval      34
d-set      32—33
echo      144
Equivalence, order      49
Equivalence, uniform      162
Event      144
Form, Minkowski      8
G-structure      172
Gage      160
Gaufi      150
Group, $GL(n, \mathbb{R})$       8
Group, affine      8
Group, conformal      11
Group, euclidean      8
Group, Lorentz      8
Group, O(n)      8
Group, orthogonal      8
Group, Poincare      8
Group, translation      8
Homogeneity property, first      61
Homogeneity property, second      65
Homogeneity property, third      116
Hypersphere, separating      117
Hypersphere, spacelike in $\check{D}$       75
Hypersphere, spacelike in D      61
Interval, $\check{D}-$       75
Interval, D-      34
l-complete      18
l-connected      20
l-convex      34
l-polygon      21
l-polygon ascending      23
l-polygon descending      23
Lemma, polygon      23
Lemma, relativization      71
Light ray, backward      26
Light ray, forward      26
Light ray, inner      38
Light rays      16
Light rays, new      81—90
Light rays, space-time paths of      16
Local commutativity      4
Local cones      74
Manifold, differentiable      9n 10 172n
Manifold, smooth      10
Manifold, topological      10
Mantle operator      75
Map, $\Pi$       112
Map, fibre-preserving      171
Map, standard      54
Message      144
Metric in general relativity      10
Metric, Euclidean      8
Metric, pseudo-Riemannian      10
Metric, Riemannian      9 10 172
Microcausality      4
Missing sets      71
Notations, $\ell$       76
Notations, $\xi, \eta, \zeta$       76

Notations, except x, y, z      76
Notations, special to chap.      6
Notations, x, y, z      76
Operator, mantle      75
Order interval closed      28
Order interval open      28
Order isomorphism      125n
Order, causal      16
Order, completion      73
Order, equivalence      49
Order, isomorphism      125
Order, partial      16
Order, strict partial      16
Order, terminology      16
Order, total      16
Order, uniformity, Hausdorff Order, uniformity, property      70
Order, uniformity, on D-sets      70
Order, uniformity, topology of      71
Order-convex      32
Particle      144
Point, timelike      27
Points, pair of lightlike      30
Points, pair of spacelike      30
Points, pair of timelike      30
Polygon, ascending      23
Polygon, descending      23
Property S      30
Property S, global      98
Quotation, Cantor      154
Quotation, Dauben      154—155
Quotation, Ehlers, Pirani and Schild      138
Quotation, Hilbert      137
Quotation, Kronheimer and Penrose      138
Quotation, Weyl      4 8—9 12n
Quotation, Wigner      155
Relation, antisymmetric      16
S-space      30
Segment, boundary      54
Segments of light rays, closed      21
Segments of light rays, open      21
Separation, property, Jordan — Brouwer      109
Sets, D-      32—33
Sets, missing      71
Space, anti-de Sitter      22n
Space, completely regular      48
Space, cushion-free      129—132
Space, de Sitter      22n
Space, regular      48
Space, topological, completely uniformizable      164
Space, topological, disconnection of      58
Space, topological, discrete      58
Space, topological, separation of      58
Space, topological, totally disconnected      58
Space, Tychonoff      48
Space, uniformizable      68
Structure, (Weyl) projective      12
Structure, conformal      10 173
Structure, conformal, on Riemannian manifolds      173
Structure, differentiable, of D-intervals      120
Structure, Euclidean      8
Structure, G-      172
Structure, Lorentz      10 172
Structure, Minkowski      8
Structure, O(1, n-1)      see “Structure Lorentz”
Structure, O(n)      see “Metric Riemannian”
Subset, decreasing      22
Subset, increasing      22
Tensor, conformal      11
Tensor, projective      12
Tensor, Weyl      11
Theorem, generalized Jordan curve      109
Theorem, timelike points      43
Topology, Alexandrov      139
Topology, on M      73
Topology, order      46
Topology, uniform      68 161
Transformations, affine      8
Transformations, conformal      11
Transformations, conformal on Minkowski space      11
Transformations, coordinate on base space      169
Transformations, Lorentz      8
Uniform space, complete      164
Uniform space, precompact      165
Uniform space, sequentially complete      164
Uniform space, totally bounded      165
Uniform space, uniform completion of      164
Uniformity covering      160
Uniformity diagonal      159
Uniformity on ordered spaces, terminological convention      68
Uniformity order, Hausdorff property      70
Uniformity order, on D-sets      70
Uniformity order, topology of      71
Uniformity pseudometric      158
Uniformity relative      162
Uniformizability theorem for ordered spaces      68
Uniformizability, complete of ordered spaces      69
Uniformizability, complete, Shirota's theorem      69
ZFC      165n

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