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Язык: 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 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
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