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Truss J.K. — Foundations of Mathematical Analysis
Truss J.K. — Foundations of Mathematical Analysis

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Название: Foundations of Mathematical Analysis

Автор: Truss J.K.

Аннотация:

Foundations of Mathematical Analysis covers a wide variety of topics that will be of great interest to students of pure mathematics or mathematics and philosophy. Aimed principally at graduate and advanced undergraduate students, its primary goal is to discuss the fundamental number systems, N, Z, Q, R, and C, in the context of the branches of mathematics for which they form a starting point; for example, a study of the natural numbers leads on to logic (via Godel's theorems), and of the real numbers (as constructed by Cauchy) to metric spaces and topology. The author offers a refreshingly original and accessible approach, presenting standard material in new ways and incorporating less mainstream topics such as long real and rational lines and the p-adic numbers. With a discussion of constructivism and independence questions, including Suslin's problem and the continuum hypothesis, the author completes a wide-ranging consideration of the development of mathematics from the very beginning, concentrating on the foundational issues particularly related to analysis.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 362

Добавлена в каталог: 04.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^{p}$ space      272
$N_{0}$-categorical      93
$N_{\alpha}$-categorical      220
$\epsilon$-least      25
$\epsilon$-minimal      26
$\omega$-consistent      18
$\sigma$-algebra      268
$\sigma$-algebra generated      268
$\v{C}ech$      134
1-1 correspondence      1 3
1-1 function      3
2-dimensional      172
Abel      193
Abelian group      38
Absolute      306
Absolute value      70 102 122
AC      see "Axiom of choice"
Addition      10
Addition formulae      167
Addition of cardinals      34
Additivity      262 267
Affine geometry      83
Aleph      36
algebraic      178 204
Algebraic closure      180 332
Algebraic equation      95 172 197
Algebraic number      211
Algebraic number field      58
Algebraically closed      141 173
Algebraically closed field      141 172 203
Algebraically dependent      219
Algebraically independent      209 219
Algorithm      57 71 222
Almost certain      262
Alternating group      185
Analytic set      293
angle      170
Antichain      118
Anticlockwise      170 202
antisymmetric      15
Apartness      316
Approximation      148 157 212 233 295
Archimedean      70 101 111
Area      148 262
Area under a curve      271
Argand diagram      174
Argument      175
Arithmetic hierarchy      292
Arithmetization      12 17
Aronszajn tree      119
Array      51
Ascending chain condition      54
Associate      53
Associative      38
asymmetric      24
Auxiliary cubic      201
axes      170
Axiom      7 13
Axiom of Choice      22 32 132 300 315 326
Axiom of choice for families of countable sets      327
Axiom of choice for finite sets      327
Axiom of Countable Choice      277
Axiom of Dependent Choices      328 332
Axiom of extensionality      5
Axiom of foundation      326
Axiom of infinity      27
Axiom scheme      13
Axiomatic set theory      28
Axiomatizable      21
Back      93
Back-and-forth      92 254
Baire category      161
Baire category theorem      258 332
Baire space      232
Baldwin      220
Banach — Mazur game      285
Banach — Tarski      32
Bar induction      333
Bartoszynski      287
Base for a topology      107
Base of neighbourhoods      107
Basic open set      107
Basis      9 83
Bernstein's lemma      211
Beth model      312
Bijection      3
BINARY      79
Binary operation      10 38
Binary relation      3
Binary sequence      232
Binary tree      234
Binomial coefficient      91
Binomial theorem      91 225
Bisection      234
Bishop      309
Bold face hierarchy      291
Boolean algebra      254 304 326
Boolean prime ideal theorem      328
Boolean-valued model      304
Borel hierarchy      292
Borel set      269
Bound variable      13 329
Boundary      106 249
Bounded      97 146 151
Bounded closed set      263
Bounded measurable set      270
Bounded open set      263
Bounded sequence      122
Bounded set      122
Branch      118 294
bridges      309
Brouwer      308 333
Brouwer's principle      318
Burali-Forte Paradox      5 26
Cancellation      34 52 65 137 327
Canonical      4 22 87
Cantor      5 22 35 92 289 326
Cantor discontinuum      235
Cantor space      232 278
Cantor ternary set      235 269
Cantor — Bendixson derivative      290
Cantor — Bendixson rank      289
Cantor — Bendixson Theorem      288
Cantor's theorem      35 93 114
Cardano      193
Cardinal arithmetic      288
cardinal number      5 22 34
Cardinality      5 34
Carrying      139
Cartesian axis      150
Cartesian product      3
Categorical      8
Categoricity      7
Category      258
Cauchy      108 125
Cauchy completion      136
Cauchy criterion      129 162
Cauchy sequence      126 127 314
Cauchy — Schwartz inequality      123
Cauchy's theorem      202
Cayley      183
Chain      33 118
Chain rule      156
Characteristic      80 220
Choice function      32 143
Choice sequence      313
Church — Kleene $\omega_{1}$      293
circle      148 165 170
Circumference      148 170 275
Circumscribed polygon      149
class      1
Classical logic      328
Clopen      108 110
Closed      108 146
Closed ball      121
Closed bounded interval      134
Closed contour      202
Closed disc      106
Closed interval      108
Closure      107
Closure operator      83
Closure under an operation      42
Co-ordinate      3 176
Co-ordinatewise      139
Coanalytic set      293
Code      18
Coding      16 49
Cohen      47 117 301
Cohen's method of forcing      288
Colour      252
Comeagre      258
Commensurable      57 111
Common denominator      71
Common refinement      270
Commutative ring      50
Compact      101 105 109 134 143 232
Compactness Theorem      329
Comparable      118
Comparison Test      163
Compatible      118 303
Complement      106
Complete Heyting algebra      320
Complete metric space      128 139 177 258
Completed totality      308
Completeness theorem for first order logic      331
Completing the cube      197
Completing the square      197
Completion      95 126 128
Complex analysis      173 201
Complex number      172
Complex plane      165 174
composition      102
Comprehension principle      1 5
Computable      222
Condensation point      289
Condition      303
Congruence      45 51
Congruent      148
Conjugete      174 184
Connected      109
Consistency strength      29
Consistent      17 303
Constant function      104 156
Constant polynomial      87 177
Constant sequence      131
Constant symbol      329 330
Constantly irrational      322
Constantly rational      322
Constructible set      299
Constructible universe      296 299
Constructive      132 211 258
Constructive analysis      308
Constructive functional analysis      309
Constructive recursive analysis      316
Constructivism      308
Continued fraction      223 237
continuous      95
Continuous function      102 144 210 318
Continuous image      146
Continuous on the left      104
Continuous on the right      102
Continuous real-valued function      260
Continuum Hypothesis      260 288
Continuum problem      22
Contour integration      202
Contradiction      1 298 309
Converge      72 163
Convergence      128 176
Convergence test      162
Convergent sequence      73 127
Converse relation      29
Coprime      90
Cosecant      169
Coset      61 276
Cosine      162 175
Cotangent      169
Countable      35
Countable additivity      283
Countable antichain condition      117 119
Countable axiom of choice      327
Countable chain condition      119 306
Countable dense subset      246
Countable limiting process      272
Countable limits      152
Countable modal      114
Countable order-types      94
Countable sequence      136
Countable subadditivity      262
Countable transitive model      301
Countable union of rectangles      271
Countably complete ideal      279
Counting      22 24 121
Counting pattern      23
Course-of-values induction      28
Cover      108
Cube root      193 208
Cube-free      208
Cubic equation      197
Cut      99
CYCLE      184
Cycle pattern      154
Cyclic      43
De Morgan's laws      2 328
Decidable      11 310
decimal      71
Decimal expansion of $\pi$      311
Decimal notation      222
decimal point      74 222
Decreasing sequence      128
Dedekind      1 7 98 110
Dedekind completion      98 136
Dedekind cut      98 133
Definable class      300
Definable map      232
Definable set of reals      286 291
Definition by induction      9
Definition by recursion      9
Definition by transfinite induction      27
Degree      88 178
Dense      100 128 211 258 303
Dense linear ordering without endpoints      92 220
Dense open      258 303
Dense-in-itself      259 289
Densely linearly ordered      92 100 243
density      95
Denumerable      35
Derivative      155
Derived function      155
Derived sequence      237
Descending chain condition      54
Descriptive set theory      288 291
Diagonal argument      114
Diagonal of a square      111
Diameter      170 256
Differentiable      155
Differential equation      229
Differentiation      147 153
Differing at finitely many points      73
DIMENSION      85 178 232 249
Diophantine equation      223
1 2 3 4
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