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Gleason A. — Fundamentals of Abstract Analysis
Gleason A. — Fundamentals of Abstract Analysis

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Название: Fundamentals of Abstract Analysis

Автор: Gleason A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 416

Добавлена в каталог: 18.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\epsilon$-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 $\mathbf{R}$      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 $\mathbf{R}$ or $\mathbf{C}$      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 $\mathbf{R}$      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 $\mathbf{C}$      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 $\mathbf{R}$ and $\mathbf{C}$      180ff
Decimal representation of numbers      220
Decreasing sequence      161
Dedekind      84 121 128
DeMoivre      129
DeMorgan's laws      35 52
Dense, $\epsilon$-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 $\mathbf{R}$ or $\mathbf{C}$      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 $\mathbf{R}^{*}$      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 $\mathbf{R}$      280
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