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Reid M., Szendroi B. Ч Geometry and Topology
Reid M., Szendroi B. Ч Geometry and Topology

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Ќазвание: Geometry and Topology

јвторы: Reid M., Szendroi B.

јннотаци€:

An introduction to the ideas of geometry and includes generous helpings of simple explanations and examples.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2005

 оличество страниц: 240

ƒобавлена в каталог: 11.06.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abstract group      169
Affine frame      69 71
Affine geometry      62Ч72 95
Affine group Aff(n)      102 161 170
Affine linear dependence      68 71
Affine linear map      8Ч9 27 68Ч69
Affine linear subspace      29Ч30 62Ч68 70Ч72 91
Affine space $\mathbb{A}^n$      62 63 68 95 170
Affine space $\mathbb{A}^n$ in projective space      82
Affine span      62 66Ч67
Affine transformation      xvi 8Ч9 68Ч70 91
Algebraic topology      xv 113 130
Algebraically closed field      136Ч137
angle      1 5Ч6 27 62 69 95
Angle bisector      23 25
Angle of rotation      15Ч18
Angle sum      19Ч20 34 40 51Ч56
Angle, signed      6
Angular defect, excess      see angle sum
Area      40Ч41 51Ч56
Associative law      28 32 94 169
Axiomatic projective geometry      86Ч88 164 168 177
Ball      58 109 138 146
Based loop      131Ч133 136Ч137
Basis for a topology      124Ч126
Bilinear form      see Euclidean inner product Lorentz 162 183Ч185
Bolyai's letter      166
Centre of rotation      15
Centroid      21 69Ч71
Circumcentre      21 22
Closed      see compact versus closed 58 75 108 111 113 138 148
Closed and bounded      115Ч129 146
Closed map      129Ч130
Closed, diagonal      127Ч128
Cofinite topology      108 111 127
Commutative law      15 17 28 32
Compact      see maximal compact sequentially xv 75 115Ч117 121 133Ч138 143 146 152
Compact Lie group      146 147 160
Compact surface      119 177Ч178
Compact versus closed      128Ч129
Compactification      75
Complex number      12 27 136 188
Composite of maps      26Ч33
Composite of reflections      16 29Ч31 33 58
Composite of rotation and glide      33
Composite of rotation and reflection      31
Composite of rotations      27 33
Composite of translations      27
Congruent triangles      19 25 55
Connected      see path connected simply 113Ч115 117 138 148 149 152 153
Connected component      114Ч115 122 144 148 149 153 160 161
Connected Lie group      160
continuous      xv 5 68 91 100 142Ч144 148 149
Continuous, family of paths      131Ч132
Contractible loop      130Ч133 136 141
Coordinate changes      xiv
Coordinate frame      xiv 1
Coordinate geometry      xiii xvi 168
Coordinate system      xiv 4
Coventry market      92Ч93
Cross-ratio      79Ч81 90 106
Curvature      34 40 49 93 167 177 178 182
Desargues' theorem      82Ч84 88 90
DIMENSION      66 67 70 76 144 145 160
Dimension of a Lie group      144Ч146 148 161
Dimension of intersection      67 69 72Ч73 77 81 83 88
Direct motion      10 15 17 148 151Ч152
Disc      111 122 130 133 139
Discrete topology      108 110 127 143
Distance      see Euclidean distance hyperbolic metric shortest spherical
Distance function      1 2 4 6 7 35 62 95 180 181 183
Duality      85Ч86 90
Einstein's, field equations      see general relativity 93
Einstein's, relativity principle      see special relativity 174
Electron      xvi 143 154Ч159 175
Empty set      68 70 72 73 76 108 124
Erlangen program      xivЧxv 95Ч96 112 170Ч171
Euclid's postulates      see parallel postulate 165Ч167
Euclidean angle      45
Euclidean distance      1 2 4 116 151
Euclidean frame      1 14 25 40 145
Euclidean geometry      4 19 25 34 45 47 69 95 166
Euclidean group Eucl(n)      xvi 159 161
Euclidean inner product      2 5 9 24 43 58 184 185 187
Euclidean line      4
Euclidean motion      see motion 9 10 14 24 25 47 92 144
Euclidean plane $\mathbb{E}^2$      6 33
Euclidean space $\mathbb{E}^n$      1 4Ч10 29 35 180
Euclidean translation      19
Euler number      140 177
Family of paths      131
Feuerbach circle      23
Frame      see affine frame coordinate Euclidean orthogonal projective spherical
Frame of reference      see projective frame
Fundamental group      xv 113 130 159
Fundamental theorem of algebra      136
Galilean group      93 172Ч173
General linear group GL(n)      xv 95 99 101 105 124 143 145 147 148 160 161 171
General relativity      93 167 176 178
Generators      29 100Ч101 103 106
Genus      120 139 177
Geodesic      see shortest distance
Glide      15Ч17 24 31Ч33 40 47 98
Glide reflection      see glide
Glueing      see quotient topology
Great circle      see spherical line
Group      see abstract group fundamental Galilean general Lie Lorentz Poincare projective reflection rotation spinor topological transformation unitary
Half-turn      12 32
Hausdorff      109 110 127Ч130 139 152
Heine Ч Borel theorem      116
Hermitian form      153 156 160 163 188
Homeomorphism      107 111 113 117 119Ч121 130 132 134Ч136 138 139 147 149 152 153 160 177
Homeomorphism criterion      111 130 142 152
Homeomorphism problem      xv 113
Homogeneous space      169Ч170
Hyperbolic distance      43 46 58
Hyperbolic geometry      4 20 34 36 41Ч167
Hyperbolic line      43 46Ч50 60
Hyperbolic motion      46 144
Hyperbolic plane $\mathcal{H}^2$      39 47Ч49 58Ч61 180
Hyperbolic sine rule      59
Hyperbolic space      35 42 51 104
Hyperbolic translation      47 58 61
Hyperbolic triangle      44 51 58 59
Hyperbolic trig      35 44Ч45
Hyperplane      29 30 66 67 76 78 81 82 89 96
Hyperplane at infinity      88
Ideal point      see infinity point
Ideal triangle      51 53Ч56
Incentre      23 25
Incidence of lines      34 40 47 69 84
Indiscrete topology      108 111 139
Infinity, hyperplane at      72 73 76 82 90
Infinity, point at      48Ч49 51 53 55 59 73 75 76 79
Intersection      see dimension of intersection 108
Intrinsic curvature      34 40 177
Intrinsic distance      40
Intrinsic unit      34 49
Isometry      see motion preserves 4 6 112 181
Klein bottle      xiv 139
Length of path      5
Lie group      see compact Lie group 142Ч164 169
Line      4 65
Line, hyperbolic      44
Line, segment      3 65
Line, spherical      35
Loop      107Ч137 140 159
Lorentz basis      44 55 185 186 188 189
Lorentz complement      48 186
Lorentz dot product $\cdot_L$      43 184 186
Lorentz form $q_L$      42 47 184 186 189
Lorentz group      93 159 161
Lorentz matrix      42 46Ч47 161 188 189
Lorentz norm      44 184 186
Lorentz orthogonal matrix      187
Lorentz reflection      47
Lorentz space      42 46 188
Lorentz transformation      47 54 92 144
Lorentz translation      see hyperbolic Lorentz
Lorentz, orthogonal      44
Lorentz, pseudometric      42 58 174
Maximal compact subgroup      160
Mercator's projection      139 164 179
Metric      180Ч182
Metric geometry      64 177
Metric space      1 4 38 180Ч182
Metric topology      109 125 143 152
Minimum over paths      5 180
Moebius strip      xiv 107 118Ч119 122 139
Motion      xiv 1 6 7 9Ч11 14Ч19 24Ч26 28Ч34 38Ч40 46 47 58 61 93 95 97 98 100 103 105 106 144 149 151 152 154 158 161
Mousetrap topology      122Ч123
Musee Grevin      103 105
Newtonian dynamics      93 161 172Ч173
Non-Euclidean geometry      34Ч61 167
Normal form of a matrix      10Ч13 18 29 98Ч99 148 189
Open set      108Ч111 113Ч115 117 118 121 125 143 148
Opposite motion      10 15 17 148
Orthocentre      22Ч23
Orthogonal      see Lorentz -
Orthogonal axes      1
Orthogonal complement $V^{\perp}$      13 47 145 171 185
Orthogonal direct sum      151
Orthogonal frame      39
Orthogonal group O(n)      144Ч152
Orthogonal line      158
Orthogonal magnetic field      154 158
Orthogonal matrix      7 9Ч13 24 29 39 99 144 146Ч149 159 187
Orthogonal plane      29
Orthogonal transformation      9 92 99 187
Orthogonal vector      5 29 37 151 162 185
Pappus' theorem      84Ч85 88 90
Parallel axes      31
Parallel hyperplanes      17 64 66 67
Parallel lines      15Ч17 20Ч23 27 34 40 49 62 68 70 73 82 166
Parallel mirrors      103
Parallel postulate      20 49 60 166
Parallel sides      31
Parallel vector      16 96
Path      see length of path minimum 114 131 159
Path, connected      114 120 132 141 149
Perpendicular bisector      16 21 22 24 29 30 57
Perspective      73 74 81Ч83 88 90
Physics      xv xvi 93 160 172Ч179
Poincare group      173Ч176
Point at infinity      see infinity point
Preserves distances      6Ч7 24 39 181
Principal homogeneous space      see torsor
Pringle's potato chip      58 178
Product topology      126Ч127 139 143
Profinite topology      125 126
Projective frame      78 79 90 106 146
Projective geometry      72Ч91
Projective linear group PGL(n)      77 95 105 106 144 146 171
Projective linear subspace      73Ч77
Punctured disc D*      120 130 133 136
Quadratic form      5 9 42 123 150 151 183
Quaternions      149Ч152
Quotient topology      110 117Ч119 121Ч125 139Ч140 144 152
Reflection      1 11 15Ч17 24 27Ч30 33 34 40 58 103 105
Reflection group      103Ч105
Reflection matrix      7 10 24 42 144
Relativity      see special relativity general 161
Rigid body motion      see motion
Rotary reflection      33 40
Rotation      1 11 15Ч18 24 25 27 29 31Ч34 39 40 47 97 100 103 142 143 149Ч152 154 158 161
Rotation group      152
Rotation matrix      7 10 42 144
Rubber-sheet geometry      xiv 107
Sequentially compact      115Ч116 138
Shortest distance      see minimum over paths 4 5 40 46 58
Similar triangles      21Ч23
Simplex of reference      see projective frame
Simply connected      130 132 146 160
Spacetime      93 172Ч176 178 179
Special linear group SL(n)      159 175
Special orthogonal group SO(n)      149 152
Special relativity      xv 93 144 173Ч174 178
Special unitary group SU(n)      153 176
Sphere $S^2$      35 36 39 40 43 56 58 113 180 181
Sphere $S^n$      57 58 116 121 122 145 151
Spherical disc      56
Spherical distance      36Ч38 40 56 116
Spherical frame      34 40
Spherical geometry      4 20 34Ч41 45 56 57 164 167 182
Spherical line      39 40
Spherical motion      38 39
Spherical triangle      37Ч38 40 41 57 182
Spherical trig      37 167
Spin      143 154 155
Spinor group Spin(n)      153 159
Standard model      176
Subspace topology      117 121 128 144 147 152
Symmetry      92Ч95 160 164 169 173Ч176
Topological group      143Ч144 159
Topological property      xv 113 127 131 136 167
topology      94 107Ч141 143
Topology of $S^3$      152
Topology of $\mathbb{P}^n$      90 121 139
Topology of SO(3)      142 143 149
Torsor      169Ц170
Torus      119 120 139 177 178
Transformation group      26Ч33 92 94Ч96 101 104 112 142Ч163
Translation      1 15Ч19 25 29 31Ч33 39 68 97 98 100Ч103 106 158 161
Translation map      125
Translation subgroup      101 105
Translation vector      15 24 27 31
Triangle inequality      1Ч5 38 45 180
Trichotomy      177Ч179
Ultraparallel lines      48Ч51 59 61
UMP      see universal mapping property
Unitary group      153 176
Unitary matrix      153 158 188Ч189
Unitary representation      175
Universal mapping property      118 139 152
Winding number      xv 107 130Ч137
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