James I.M. (ed.) — Topological and Uniform Spaces :: Электронная библиотека попечительского совета мехмата МГУ

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James I.M. (ed.) — Topological and Uniform Spaces

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Название: Topological and Uniform Spaces

Автор: James I.M. (ed.)

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 163

Добавлена в каталог: 16.12.2008

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

Предметный указатель

$T_{0}$       83
$T_{1}$       71 72 75 83 143
Accumulation point      133—139 151
Addition      28 33—36 55 60 94
Adherence point      12 13 17 20—23 29 60 65—68 74 75 78 105 106 109 110 133—136 149
Adherence set      66 67
Affine transformation      28 29 44 65 94 97
Antidiagonal      45 139
Axioms of topology      9—11
Basic neighbourhood      16 20 28
Bijection      1 27 29 30 52 76
Bilinear function      35
Binary expansion      142 143
Binary operation      25 36
Bounded function      70 154
Bounded metric      59 90
Bounded set      59 61 64 65 115 119 157
Bounded uniformity      100
Bourbaki, N.      62 76
Box topology      31 39 70
Cartesian product      3 30 38 67 92
Cauchy filter      107—112 148—157
Cauchy sequence      107—109 112 150—155
Centre      128
circle      47 56 119
Closed ball      19 20 21 64 76 118 122
Closed covering      45 46 60 112
Closed function      53 56—64 68 70 73—76 131
Closed neighbourhood      16 72 73 76 78 81—84
Closure      12 13 20—23 27 32 38—40 51 52 57 66—68 74 77—79 81—83 89 99 103—105 116—118 132 133 141 144 145 154—157
Closure point      12
Cocountable topology      29
Cofinite topology      5 8 11 12 23 26 30 40 63 80 105 114 128
Coherent system      17—20 66 101
Coincidence set      74 116
Coinduced topology      48—50
Coinduced uniformity      98
Collapsing      50 76 79
Collins, P.J.      126
Commutative      5 74 88 91 157
Compact space      62—70 76—85 105—107 113 115 127—131 136 139 146 147 153
Compactly regular      82 83 157
Complete family      14 30 32 55 78 130
Complete metric space      150 151 154—157
Complete uniform space      148—157
Completely regular      140—143 146
complex numbers      30 35 47
composition      4 26 54 87 91
Conjugation      37 38 120
Connected space      114—117 120 121 128
Connectedness component      118—120 123 124
Constant function      26 40 70 90 114—117 125 128
Continuous function      26—61 63 65 70 73—75 79 80 102 107 114—125 130—137 140—149
Convergent filter      22 28 32 67 78 108 148 149 152
Convergent sequence      21 22 29 107—109 134—138 153
Convex subspace      122
Countable set      8 23 52 69 128 136—138
Countably compact      132—139
Covering      45 57 60 64 68 69 see "Open
Cylinder      76
Dense      12 23 40 51 52 74 105 116 117 136—138 149 152—156
Determinant      35 48 56
Diagonal      3 31 36 39 43 45 47 51 73 85—90 93 96 98 101—103 106 113 126 143
Diameter      59 61 90
Dilatation      28 31 35 94
Direct product      38 39 51 94
Disconnected      115 122
Discrete group      50 88 91 128
Discrete metric      18 20 59 89 138
Discrete topology      9—14 20—26 29 30 36 39 44 45 48—53 57 62 63 77 79 82—84 101 102 113—117 120 121 139
Discrete uniformity      86—89 90 100 101 109 125 126 148
Division      38 47 52
Dual family      11 68
Dyadic expansion      142—144
Elementary filter      5—8 22 109—112 136 150
Embedding      41—44 52 54 57 63 64 73—77 80 119 131 141 143
Entourage      85—113 125—127
Equivalence class      4 36 50 117
Equivalence relation      4 39 50—52 76 79 83 89 98 100 117 118 123 124 128 147 155
Euclidean metric      18—21 59 84 90 100
Euclidean topology      20 36 39 44 46 52 58—61 64 77 84 115 118 125 128 130 157
Euclidean uniformity      87 88 91 94 97 100 107 108 112 126
Exponential function      97 100 108
Factor group      55 56 98 125
Factor space      51 55 75—78
Filter      5—8 21—23 28 39 65—68 85—87 109
Filter base      6 8 16 19 87 88 106 113 128
Final topology      41
Finite set      8 11 26 63 89 98 100 108 110 139
First countable      130 135—139
Function space      67 111
Functionally Hausdorff      140 147
Functionally normal      140
Functionally regular      140
Functionally separated      140—147
Fundamental system of neighbourhoods      18 101
General linear group      48 65
Generating family      13—14 19 27—32 41—46 55 70 86 120 131 137 138 141
Graph      43 64 73 75 83 96
Hausdorff quotient space      79 105
Hausdorff space      62 72—85 103 106 113 127—129 133 136—139 147 157
Heine — Borel theorem      64 65 153
Hilbert sequence space      19 150
Homeomorphism      29—31 34 35 45—52 56 62 76 79 102 119 125 141
Homomorphism      25 37—39 44 91 98
Idempotent      12
Identification space      50
Identity relation      4
Indexing set      1 3 33 39 93
Indiscrete topology      10
Induced topology      41—44 48 50 95 103
Induced uniformity      95 102 110
Infimum      20 65 115 143 145
Infinite set      11 21 105 113 133 136 151
Initial topology      41 42
Injection      1 24 42 43 54 57 73 95 96 156
Interior      12 13 23 32 39 40 54 83 104
Interior function      53
Interior point      12 13 17 119
Intermediate Value Theorem      116
interval      14—16 27 44—46 50 56 59 83 97 116 119
Interval topology      15 16 27 44
inversion      36 46—48 51 55 91 94 157
Irrationals      16
Isometry      28 153—155
Isomorphism      37 56
Juxtaposition      123
Kelley, J.L.      83
Lebesgue number      69
Left inverse      43 96
LIMIT      21 22 153
Limit point      22 23 29 32 75 109 110 134 150—153
Lindeloef      131 132 139
Linearly ordered set      14
Locally connected      120 121 124—128
Locally pathwise-connected      124 125
Lower central series      39
Lower limit topology      15
Lower Sorgenfrey topology      15
Matrices      30 34 35 48 94
Matrix multiplication      35 48
Maximum      46 94
Metric      18 24 28 33 59 88 90 155
Metric completion      154 155
Metric space      18—21 27 28 45 65 69—71 77 80 85 91 101 102 108 126 137 138 150—155

Metric topology      20 33 59 71
Metric uniformity      88
Minimal Cauchy filter      112 113
Minimum      33 46 59 69 90 94 151
Modular group      56
Multiple induced topology      42
Multiplication      28 34 35 47 55 61 91 94 137 138
Negative      36 94
Neighbourhood      13 16—17 21 23 51 66 70—73 78 79 83 100
Neighbourhood base      16 17 21 22 32 33 38 39 45 72 82 88 101—105 120 124 126 128 135—138
Neighbourhood filter      16 17 20—23 28 29 33 34 45 59 65 75 76 88 102 109 113 136 152
Neighbourhood of diagonal      36 106 107 113
Nesting condition      8 151
Net      90 108 151
Norm      33
Normal space      80—82 84 132 144—147
Normal subgroup      38—40 55—56 98 119 120 125 128 157
Open ball      19—21 47 59 88 101 108 118 122 138
Open covering      45 46 60 68 69 81 113 128 131—134 151
Open function      53—56 75 130
Open neighbourhood      13 16 26—28 34 37—40 51 56—60 63 70—73 77—83 120 124 128 132 140 141
Orbit space      50
Order      14
Order-preserving function      27
Ordered set      14 15 27 44
Orthogonal group      65 76
p-adic structure      88 128
Partially ordered set      14
Partition      102 118
Path      121—125
Path-component      123—125
Pathwise-connected      121—125
Pointwise complete      157
Pointwise convergence      112
Pointwise topology      67
Polar coordinates      76
Polynomial function      35 39
Precompact      89
Principal filter      5 7 16 20 21 66 109 155
Product neighbourhood      32
Product set      30 31
Product topology      30—33 38 39 45 63 67 103 104 131
Product uniformity      93 98 103 111
Projective space      50 52
Proper function      70
Property S      126 127
Punctured circle      119
Punctured complex line      47 158
Punctured open ball      21
Punctured real line      46 94 97 118
Punctured sphere      64
Quasicompact      62
Quotient map      49—57 82 121 128
Quotient space      50—52 75 76 79 124 128 147
Quotient topology      50 51 55 117
Quotient uniformity      98
Rational line      16 29 46 47 77 82 112 115 118 125 128 136 157 158
Ray      15
Real line      4 16 18 20 23 24 31 36 39 46 47 50 53 56 59 61 64 65 68 77 82 84 87 88 116—120 124
Real n-space      18 21 36 46 47 59 64 65 88 118—121 124 146
refinement      6 7 9 13 21—23 67 77 109 112 152
Reflexive      4 36 78 79 87 89 118
Regular space      76—83 89 104—106 132 147
Regularly closed      23
Regularly open      23
Relation      3—5 36 83 88 100
Relative topology      44—46 51—54 65 67 103 139
Relative uniformity      97 98 103 105
Restricted product neighbourhood      32 78 141
Restricted product set      30 32 93 117 120
Reverse path      123
Reverse relation      4
Right inverse      50 52
Saturation      2 55 57 78 79
Scalar division      47
Scalar multiplication      35 47
Second countable      120 130—132 136 138
Separable      136—139
Separated quotient space      98 99 105 152 156
Separated uniform space      89 94 103 106 112 148 152—157
Separation conditions      71
SEQUENCE      5 19—22 33
Sequentially compact      134—136 139
Sequentially complete      150 151
Sierpinski      10 20 30 39 80 121 126
Small      89 109—112 126 127 151 156
Sorgenfrey line      15 44 139
Sorgenfrey plane      44 139
Sphere      21 47 50 64 76 100 118 122
Squaring function      35 53 57 91
Stationary path      123
Stereographic projection      47
Structure-preserving function      25 53 90
Subcovering      45 68 131 132
Subgroup      38 39 45 51 52 55 70 74—78 98 117 128
Subsequence      5 67 108—110 134 135
subspace      41 44—48 64 73 80 97 98
Supremum metric      19 65 154
Surjection      1 49 53 54 63 76 80 99 115 121 124 125 130 133 137
Surrounding      85
symmetric      4 36 78 87—89 99 103—105 118 127
Symmetric neighbourhood      38 39
Tietze theorem      145 146
Topological equivalence      29
Topological group      36—40 45 55 64 75 78 82 85 88—91 94 98—102 105 107 117 119 125 126
Topological product      30—36 39 42 55 65 73 80 103 117 120 121 131—134 137 140 141
Topological space      9—84 101—158
Topologists' sine curve      122
Topology of pointwise convergence      67
Topology of uniform convergence      111
Totally bounded uniformity      89 90 94 98 108—111 127 137 138 151 153 157
Totally disconnected      115 118 128 129
Trace      6 44—46 66 82 97 105 106 152
Transitive      4 36 42 49 78 79 86 89 95 123
Translation      28—31 34 37 51 94 120
Trivial topology      10—12 22—26 30 36 42—44 48 51—53 57 71 77—80 101 114 120 128
Trivial uniform space      86—90 96 101 109 148
Tychonoff theorem      64 67 68
Ultrafilter      7 8 23 67 110—113
Uncountable      40
Uniform completion      155—158
Uniform embedding      95—97 155 156
Uniform equivalence      92 97 102 153—156
Uniform neighbourhood      101—109 113 126
Uniform product      92—97 100 125 149 157
Uniform space      85—113 142 148 155
Uniform topology      101—104 113 142
Uniformity base      87—90 96 101 104—107 126 156
Uniformity of pointwise convergence      111
Uniformity of uniform convergence      111 149
Uniformization      106 107 111 141—143
Uniformly Cauchy      112 149
Uniformly complete      149 150
Uniformly connected      125 126
Uniformly continuous function      90—100 102 107 110 112 125 143
Uniformly convergent      112
Uniformly homogeneous      92 93
Uniformly locally connected      127
Uniqueness      22
Unit circle      18
Upper limit topology      15
Upper Sorgenfrey topology      15 44
Urysohn theorem      144 145
Weak transitivity      88 98 99
Whyburn, G.T.      126

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