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| Hu S.-T. — Introduction to contemporary mathematics |
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| Предметный указатель |
Abelian group 106
Absolute value 60 71 83
Accumulation point 174
Addition 47 56 65 78 84 92 110 127
Addition, Boolean 96
Addition, coordinatewise 127
Addition, functional 111
Addition, mod p 91
Addition, usual 90
Affine geometry 159 161
Affine group 159 160
Affine property 159 161
Affine transformation 159 160
Aggregate 3
Algebra 121
Algebra, division 121
Algebra, polynomial 122
Algebraic number 83
Amplitude 88
Associative 92 121
Associative laws 11 48 57
Automorphism 99
Automorphism group 104
Ball 169
Ball, open 169
Basis 128 190
Basis, fundamental 128
Biadditive 119
Bijective function 18
Binary operation 90
Boolean addition 96
Boolean multiplication 96
Boundary 169 192
Boundary point 169 192
Bundle 158
Bundle, harmonic 158
Cancellation laws 48 57
Cantor's method 72
Cardinality 34
Cartesian power 25
Cartesian product 24 29
Cartesian square 26
Cauchy sequence 73 181
Cauchy's condition 180
Characteristic 116
Circle group 104
class 31
Class, equivalence 31
Closed function 193
Closed set 172 192
Closure 173 192
Cluster point 174 179 192
Coefficient ring 119
Collection 3
Collinear 136 142
Commutative 93 97 112 121
Commutative laws 11 48 56
Commutative triangle 23
Complement 13
complete 84
Complete space 181
Complex conjugate 87
Complex number 84
Complex plane 85 88
Composable functions 20
Composed function 20
Composite 90
composition 20
Composition, usual 91
concurrent 151 158
Condition 2 6
Condition, defining 6
Condition, necessary 2
Condition, sufficient 2
Congruence mod p 30
conjugate 87
Conjugate, complex 87
Conjunction 2
Construction 47
Construction, inductive 47
Continuity 184
Continuity, uniform 182
continuous 184 192
Continuous, uniformly 182
Converge 176
Convergent 180
CONVERSE 2
Coordinate 126
Coordinate axis 127
Coordinate vertex 152
Coordinate, homogeneous 139
Corollary 1
Countability 37
Countability, first axiom of 191
Countability, second axiom of 191
Countable 37
Countably infinite 37
Counting process 36
Cross ratio 158
De Morgan formulae 11
Decreasing function 33
Dedekind's method 72
Degree 123
Dense set 175 181
Derived set 174
Diagonal 26
Difference 50 58 67 79 85
Difference, set-theoretic 10
Directed line 136
Direction 135
Discrete metric space 168
Discrete space 189
Discrete topology 189
Disjoint 11
Disjunction 2
Distance 133 166
Distance function 166
Distributive laws 11 48 57 111
Divisible 50 60
Division algebra 121
Division ring 113
Divisor 50 60
Divisor of zero 112
Divisor, greatest common 51
Domain 15 113
Domain, integral 113
Element 4
Empty set 4
Endomorphism 99 124
Epimorphism 99
equal 6
Equipotent 34
Equivalence class 31
Equivalence relation 30
Equivalent 2
Equivalent, topologically 193
Euclidean 133 143
Euclidean geometry 150
Euclidean metric 133
Euclidean plane 143
Euclidean postulate 136
Euclidean space 25 125 167
Eventually in a set 176
Extension 22
Exterior 169 192
Exterior point 169 192
Family 3
Family, indexed 25
Field 114
Field, skew 113
| Filter 195
finite 34
First axiom of countability 191
FRACTION 62 69
Fraction, positive 69
Frechet separation axiom 194
Frechet space 194
Frequently in a set 176
Frontier 169 192
Frontier point 169 192
Function 14
Function, bijective 18
Function, closed 193
Function, composed 20
Function, continuous 184 192
Function, decreasing 33
Function, distance 166
Function, identity 18
Function, inclusion 18
Function, increasing 33
Function, induced 33
Function, injective 18
Function, inverse 18
Function, isometric 183
Function, linear 18
Function, negation 58
Function, norm 129
Function, open 192
Function, submetric 183
Function, surjective 16
Function, uniformly continuous 182
Functional addition 111
Functional multiplication 111
Fundamental basis 128
Fundamental sequence 73 181
Generator 110
Geometry 126
Geometry, affine 151 161
Geometry, Euclidean 150
Geometry, metric 150
Geometry, projective 153 164
Graph 26
Greatest common divisor 51
Group 104
Group, abelian 106
Group, affine 159 160
Group, automorphism 104
Group, circle 104
Group, isometry 150
Group, permutation 104
Group, projective 153
Harmonic bundle 158
Harmonic range 157
Hausdorff separation axiom 193
Hausdorff space 193
Hilbert space 167
Homeomorph 193
Homeomorphic 193
Homeomorphism 193
Homogeneous coordinates 139
Homomorphism 98 115 123
Homomorphism, identity 98 115 123
Homomorphism, inclusion 98 115 123
Homomorphism, proper 101
Hyperplane 137 140
Hyperplane at infinity 141
Hyperplane, coordinate 140
Hyperplane, projective 140
Ideal 115 123
Ideal, left 115 123
Ideal, nontrivial proper 115
Ideal, right 115 123
Idempotent 95
Identity 112
Identity function 18
Identity homomorphism 98 123
IFF 2
Image 15 102
Image, inverse 16
Imaginary number 84 87
Imaginary part 87
Imaginary unit 87
Imbedding 141
Implication 2
inclusion 5
Inclusion function 18
Inclusion homomorphism 98 123
Increasing function 33
INDEX 25
Indexed family 25
Induced function 33
Induction 46
Induction, complete 46
Induction, mathematical 46
Inductive construction 47
Inequality 130 131 133 166
Inequality, Schwarz 130
Inequality, triangle 131 133 166
Infinite 34
Infinite order 116
Infinite, countably 37
Injective function 18
Inner multiplication 128
Inner product 128
INTEGER 52
Integer, negative 52
Integer, positive 52
Integers mod p 32 110
Integral domain 113
Interior 169 192
Interior point 169 192
Intersection 9
interval 3
Interval, unit 3 6
Inverse 68 80 86 103
Inverse function 18
Inverse image 16
Inverse, left 103
Inverse, right 103
Invertible 103
Irrational number 72 80
Isometric transformation 144
Isometry group 150
Isomorphic 99 182
Isomorphism 99 124
Kernel 102
Klein's Erlangen program 126
Least common multiple 52
Least member 32
Left ideal 115 123
Left inverse 103
Left projection 92
Left translation 108
Left unit 94
Lemma 1
LIMIT 177
Limit point 174
Line 135
Line, directed 136
Line, projective 138
Line, straight 135
Linear function 18
Linear mapping 123
Linear order 32
Linear transformation 152
Lipschitz condition 183
Long division 91
Lowest terms 69
MAP 192
Map, constant 192
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