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James I.M. Ч Topological and Uniform Spaces
James I.M. Ч Topological and Uniform Spaces

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Ќазвание: Topological and Uniform Spaces

јвтор: James I.M.

язык: en

–убрика: ћатематика/

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

ed2k: ed2k stats

√од издани€: 1987

 оличество страниц: 163

ƒобавлена в каталог: 20.05.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$T_0$      83
$T_1$      71 72 75 83 143
Accumulation point      133Ч139 151
Addition      28 33Ч36 55 60 94
Adherence point      12 13 17 20Ч23 29 60 65Ч68 74 75 78 105 106 109 110 133 149
Adherence set      66 67
Aftine transformation      28 29 44 65 94 97
Antidiagonal      45 139
Axioms of topology      9Ч11
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      107Ч112 148Ч157
Cauchy sequence      107Ч109 112 150Ч155
Centre      128
circle      47 56 119
Closed ball      19 20 21 64 76 118 122
Closed covering      45 46 60 112
Closed function      53 56Ч64 68 70 73Ч76 131
Closed neighbourhood      16 72 73 76 78 81Ч84
Closure      12 13 20Ч23 27 32 38Ч40 51 52 57 66Ч68 74 77Ч79 81Ч83 89 99 103Ч105 116Ч118 132 133 141 144 145 154Ч157
Closure point      12
Cocountable topology      29
Cofinite topology      5 8 11 12 23 26 30 40 63 80 105 114 128
Coherent system      17Ч20 66 101
Coincidence set      74 116
Coinduced topology      48Ч50
Coinduced uniformity      98
Collapsing      50 76 79
Collins, P.J.      126
Commutative      5 74 88 91 157
Compact space      62Ч70 76Ч85 105Ч107 113 115 127Ч131 136 139 146 147 153
Compactly regular      82 83 157
Complete family      14 30 32 55 78 130
Complete metric space      150 151 154Ч157
Complete uniform space      148Ч157
Completely regular      140Ч143 146
complex numbers      30 35 47
composition      4 26 54 87 91
Conjugation      37 38 120
Connected space      114Ч117 120 121 128
Connectedness component      118Ч120 123 124
Constant function      26 40 70 90 114Ч117 125 128
Continuous function      26Ч61 63 65 70 73Ч75 79 80 102 107 114Ч125 130Ч137 140Ч149
Convergent filter      22 28 32 67 78 108 148 149 152
Convergent sequence      21 22 29 107Ч109 134Ч138 153
Convex subspace      122
Countable set      8 23 52 69 128 136Ч138
Countably compact      132Ч139
Covering      45 57 60 64 68 69 open
Cylinder      76
Dense      12 23 40 51 52 74 105 116 117 136Ч138 149 152Ч156
Determinant      35 48 56
Diagonal      3 31 36 39 43 45 47 51 73 85Ч90 93 96 98 101Ч103 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      9Ч14 20Ч26 29 30 36 39 44 45 48Ч53 57 62 63 77 79 82Ч84 101 102 113Ч117 120 121 139
Discrete uniformity      86Ч89 90 100 101 109 125 126 148
Division      38 47 52
Dual family      11 68
Dyadic expansion      142Ч144
Elementary filter      5Ч8 22 109Ч112 136 150
Embedding      41Ч44 52 54 57 63 64 73Ч77 80 119 131 141 143
Entourage      85Ч113 125Ч127
Equivalence class      4 36 50 117
Equivalence relation      4 39 50Ч52 76 79 83 89 98 100 117 118 123 124 128 147 155
Euclidean metric      18Ч21 59 84 90 100
Euclidean topology      20 36 39 44 46 52 58Ч61 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 75Ч78
Filter      5Ч8 21Ч23 28 39 65Ч68 85Ч87 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 135Ч139
Function space      67 111
Functionally Hausdorff      140 147
Functionally normal      140
Functionally regular      140
Functionally separated      140Ч147
Fundamental system of neighbourhoods      18 101
General linear group      48 65
Generating family      13Ч14 19 27Ч32 41Ч46 55 70 86 120 131 137 138 141
Graph      43 64 73 75 83 96
Hausdorff quotient space      79 105
Hausdorff space      62 72Ч85 103 106 113 127Ч129 133 136Ч139 147 157
Heine Ч Borel theorem      64 65 153
Hilbert sequence space      19 150
Homeomorphism      29Ч31 34 35 45Ч52 56 62 76 79 102 119 125 141
Homomorphism      25 37Ч39 44 91 98
Idempotent      12
Identification space      50
Identity relation      4
Indexing set      1 3 33 39 93
Indiscrete topology      10
Induced topology      41Ч44 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      14Ч16 27 44Ч46 50 56 59 83 97 116 119
Interval topology      15 16 27 44
inversion      36 46Ч48 51 55 91 94 157
Irrationals      16
Isometry      28 153Ч155
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 150Ч153
Lindelof      131 132 139
Linearly ordered set      14
Locally connected      120 121 124Ч128
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      18Ч21 27 28 45 65 69Ч71 77 80 85 91 101 102 108 126 137 138 150Ч155
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 70Ч73 78 79 83 100
Neighbourhood base      16 17 21 22 32 33 38 39 45 72 82 88 101Ч105 120 124 126 128 135Ч138
Neighbourhood filter      16 17 20Ч23 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      80Ч82 84 132 144Ч147
Normal subgroup      38Ч40 55Ч56 98 119 120 125 128 157
Open ball      19Ч21 47 59 88 101 108 118 122 138
Open covering      45 46 60 68 69 81 113 128 131Ч134 151
Open function      53Ч56 75 130
Open neighbourhood      13 16 26Ч28 34 37Ч40 51 56Ч60 63 70Ч73 77Ч83 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      121Ч125
Path-component      123Ч125
Pathwise-connected      121Ч125
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      30Ч33 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      49Ч57 82 121 128
Quotient space      50Ч52 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 116Ч120 124
Real rc-space      18 21 36 46 47 59 64 65 88 118Ч121 124 146
refinement      6 7 9 13 21Ч23 67 77 109 112 152
Reflexive      4 36 78 79 87 89 118
Regular space      76Ч83 89 104Ч106 132 147
Regularly closed      23
Regularly open      23
Relation      3Ч5 36 83 88 100
Relative topology      44Ч46 51Ч54 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 130Ч132 136 138
Separable      136Ч139
Separated quotient space      98 99 105 152 156
Separated uniform space      89 94 103 106 112 148 152Ч157
Separation conditions      71
SEQUENCE      5 19Ч22 33
Sequentially compact      134Ч136 139
Sequentially complete      150 151
Sierpinski      10 20 30 39 80 121 126
Small      89 109Ч112 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 74Ч78 98 117 128
Subsequence      5 67 108Ч110 134 135
subspace      41 44Ч48 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 87Ч89 99 103Ч105 118 127
Symmetric neighbourhood      38 39
Tietze theorem      145 146
Topological equivalence      29
Topological group      36Ч40 45 55 64 75 78 82 85 88Ч91 94 98Ч102 105 107 117 119 125 126
Topological product      30Ч36 39 42 55 65 73 80 103 117 120 121 131Ч134 137 140 141
Topological space      9Ч84 101Ч158
Topologists'sine curve      122
Topology of pointwise convergence      67
Topology of uniform convergence      111
Totally bounded uniformity      89 90 94 98 108Ч111 127 137 138 151 153 157
Totally disconnected      115 118 128 129
Trace      6 44Ч46 66 82 97 105 106 152
Transitive      4 36 42 49 78 79 86 89 95 123
Translation      28Ч31 34 37 51 94 120
Trivial topology      10Ч12 22Ч26 30 36 42Ч44 48 51Ч53 57 71 77Ч80 101 114 120 128
Trivial uniform space      86Ч90 96 101 109 148
Tychonoff theorem      64 67 68
Ultrafilter      7 8 23 67 110Ч113
Uncountable      40
Uniform completion      155Ч158
Uniform embedding      95Ч97 155 156
Uniform equivalence      92 97 102 153Ч156
Uniform neighbourhood      101Ч109 113 126
Uniform product      92Ч97 100 125 149 157
Uniform space      85Ч113 142 148 155
Uniform topology      101Ч104 113 142
Uniformity base      87Ч90 96 101 104Ч107 126 156
Uniformity of pointwise convergence      111
Uniformity of uniform convergence      111 149
Uniformization      106 107 111 141Ч143
Uniformly Cauchy      112 149
Uniformly complete      149 150
Uniformly connected      125 126
Uniformly continuous function      90Ч100 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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