|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Gleason A. — Fundamentals of Abstract Analysis |
|
|
|
| Предметный указатель |
 -dense 267
a-function 152
A-relation 152
A-set 152
a-subset 158
Absolute convergence, of infinite products 215
Absolute convergence, of infinite series 195
Absolute value of a number 133
Addition, of cardinals 156—157 159
Addition, of natural numbers 113
Addition, of positive real numbers 123
Addition, of rational numbers 117
Addition, of real numbers 126
Adherent point 231
Adherent point to a sequence 231 Ex. 2
Alternating series 182 Ex. 5
Analytic continuation 304ff 320ff
Analytic functions 287ff
Analytic functions, arithmetic combinations 300
Analytic functions, defined by power series 301
Analytic functions, definition 298
Analytic functions, local structure 334ff
AND 9—10
angles 328ff
Anticonformal 339 Ex. 7
Antisymmetric relation 70
ARC 284
Archimedean ordered field 107
Arcwise connected space 284
Argument, of a complex number 330
Argument, of a function 41
Argument, variation along a path 333
Arithmetic combinations, of analytic functions 300
Arithmetic combinations, of continuous functions 243—244
Ascending chain condition 155 Ex. 4
Associative law, for cardinals 156
Associative law, for sets 30 52
Associative law, general 186—188
Associative operation 94
Associative-commutative law 186—188 204—205
Associativity, of direct products 39 48
Associativity, of functions 44
Associativity, of relations 50 Ex. 1
assumptions 20 23
Attractive fixed point 262
Axiom 59 153
Axiom of Choice 148ff 154
Axiomatic set theory 151ff
Baire category theorem 263
Ball in metric space 226
Base, for open sets 274
Base, for open sets in a direct product 277 Ex. 3
Beman, W.W. 84 128
Biconditional 14
Bicontinuous function 250
Bijective function 45
Bijective function, continuous function on a compact space is a homeomorphism 271
Binary combinations of sets 29
Binary operations 94
Binary relation 50
Binomial coefficients 295
Binomial theorem 296
Bolzano — Weierstrass property 269
Bolzano — Weierstrass theorem 184
Bound variable 27
Bound, greatest lower 77
Bound, least upper 77
Bound, lower 77
Bound, upper 77
Boundary of a set 238
Bounded 77
Bounded above 77
Bounded below 77
Bounded complex-valued function 134
Bounded function 77 228
Bounded sequence 161
Bounded set in metric space 228
Bounded subset of C 134
Bounded totally 267
Boundedness of a continuous function on a compact space 271
Brackets 3
Branch of a multiple-valued function 323
Canonical bijection of direct product 48
Canonical models 63
Cantor's paradox 154
Cardinal (numbers) 155ff
Cardinal (numbers) of  218
Cardinal (numbers) of a separable metric space 275
Cardinal (numbers) of a set 142
Cardinal (numbers) of the continuum 157
Cardinal exponents 157
Cartesian product of two sets 39
Categorical postulate system 63
Category of a set 264
Cauchy criterion for convergence in or  180—181
Cauchy criterion for convergence in metric space 253
Cauchy criterion for convergence, of infinite products 213
Cauchy product of two series 209
Cauchy sequence 181 253
Center, of a division algebra 131 Ex. 2
Center, of a power series 293
Chains 84ff
Characteristic function of a set 157 200
Characteristic of a field 102—103
Circle of convergence of a power series 294
Circular functions 310ff
class 2
Classical double sum 208
Classification 63
Closed ball 239 Ex. 4
Closed function 243
Closed interval 279—280
Closed set 232
Closed subset of a subspace 234
Closure 233
Cluster point 231
Codomain of a function 45
Coefficients of a power series 293
Cohen 154 158
Collection 2
Commutative laws, for cardinal arithmetic 156
Commutative laws, for sets 30 52
Commutative laws, general 186—188
Commutative operation 94
Compact spaces 266ff
Comparable elements in an ordered set 75
Comparison test for convergence of infinite series 196 182
Compatible 104
Complement 34
Complete analytic function 323
Complete metric space 253ff
Complete ordered field 108ff
Complete ordered set 79ff
Completeness of space of continuous functions 255
Completion of a metric space 259
Complex exponents 325
complex numbers 129ff
Components, of a space 282
Components, of open sets in a locally connected space 283
Composition, of functions 44
Composition, of relations 50 Ex. 1
Compound symbols 3
Compute to k decimals 221
Conceptually equivalent postulate systems 61 66 71
Conditional connective 13—14
Conditionally convergent series 195
Conditionally convergent series, rearrangement of 198
Configuration 55
Configuration, notation 72
conformal 337—338
| Conformal, mapping theorem 339
Conjugate complex numbers 132
Connected spaces 278ff
Connected subsets of 280
Connected, locally 282
Connectives, logical 8ff
Consistency of postulates 26 62
Constant function 42
Continuous function 239ff
Continuous function on a connected space 279
Continuous function, definition 240
Contraction 262
Contraction, fixed-point theorem 261
Contrapositive 19
Convergence in 161
Convergence in metric spaces 229ff
Convergence, of infinite products 212
Convergence, of infinite series 191
Convex metric space 265 Ex. 7
Coordinate projections 47 54
Coordinates in a direct product 39 54
Corollary 60
Cosine function 310ff
Cosines, Law of 338 Ex. 3
Countable axiom of choice 154 Ex. 7
Countable base for the open sets 274
Countable set 143
Counterimage of a set 47
Covering 266
Criteria for the existence of limits in and 180ff
Decimal representation of numbers 220
Decreasing sequence 161
Dedekind 84 121 128
DeMoivre 129
DeMorgan's laws 35 52
Dense, -dense 267
Dense, set 239
Denumerable set 143
Derivative 288
Derived set 239 Ex. 6
Diagonal of a direct product 39
Diameter of a set in a metric space 228
Difference of two sets 34
Difference of two sets, symmetric 37 Ex. 8
Differentiability, of analytic functions 299
Differentiability, of compositions 290
Differentiability, of power series 297
Differentiability, of rational functions 290
Differentiation 287ff
Digital representatives 220
Direct product, of a family of sets 53
Direct product, of two metric spaces 225
Direct product, of two sets 39
Directed angle 329
Directed angle between two paths away from a point 336
Direction of a path away from a point 335
Disconnected 278
Discrete space 238
Disjoint sets 34
Disk of convergence of a power series 294
Distance function 223
Distributive lattice 78 Ex. 5
Distributive law, for cardinal arithmetic 156
Distributive law, for direct products 30 Ex. 4
Distributive law, for sets 30 52
Divergence in or 161
Divergence in metric spaces 229
Divergence to zero 212
Divergence, of infinite products 212
Division algebra 131 Ex. 2
Domain, of a function 41
Domain, of a logical variable 15
Domain, of a relation 50
Dominated Convergence Theorem 206
Dominates (series) 196
Dominates (sets) 136
Double limit 208
Double sequence 207 231
Double series 207ff
Double sum 208
Doubly periodic 314 Ex. 7
Duality, of interior and closure 237
Duality, of intersection and union 35—36 52
Duality, of open and closed sets 236
Dummy index 166
Dummy variables 26ff
Dummy variables, conventions concerning 162—163
Dyadic 220
Effectively finite 190
Empty set 3
Entire functions 302
Enumerable set 143
Equality 2
Equicontinuity 249 Ex. 3
Equivalence classes 66
Equivalence relations 65ff
Equivalent postulate systems 61
Eudoxus of Cnidos 121
Euler 129 331
Exclusive OR 10
Existential quantifier 16
Exponential form of a number 220
Exponential function 308ff
Exponents, in cardinal arithmetic 157
Exponents, integral 134—135
Exponents, nonintegral 324ff
Extended binary combinations of sets 30
Extended complex plane 178
Extended direct products 39
Extended real number system 174
Extension, least common 53
Extension, least common, continuity of 245 Ex. 5
Extension, of a binary operation to finite sets 186
Extension, of a continuous function 273 Ex. 17
Extension, of a function 43
Extension, of a uniformly continuous function 258
Factorial function 293
Factoring functions 67ff
False propositions 9
Family 48
Field 94ff
Field of rational functions 104
Field, complete ordered 108ff
Field, definition 96
Field, ordered 104
Finite intersection property 272 Ex. 5
Finite member of  173
Finite set 141
First element, of a simple chain 89
First element, of an ordered pair 37
First principle of induction 87
First-order predicate calculus 8
Fixed point of a function 81
Formal fractions 116ff
Formal infinite product 212
Formal infinite sum 191ff
Fractions 116ff
Freely homotopic paths 339 Ex. 12
Function 40ff
Function, defined by formula 42
Function, definition 41
Function, spaces 226
Fundamental theorem of algebra 318 339
Generating subset of a chain 86
Goedel 26 62 153 154 158
Graph, of a function 40
Graph, of a relation 49
Greatest lower bound 77
Group 135 Ex. 1
Half-open intervals in 280
|
|
|
| Реклама |
|
|
|
|
|
О проекте