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| Gleason A. — Fundamentals of Abstract Analysis |
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| Предметный указатель |
Harmonic series 196
Heine — Borel property 267 269
Heine — Borel theorem 270
Holomorphic 298
Homeomorphism 249ff
Homeomorphism of a compact space 271
Homotopic paths 339 Ex. 12
Hypothesis of the continuum 158
Idempotent laws for sets 30
Identity, element 95
Identity, function 41
Identity, map 46
If..., then ... 13
Image of a set 46
Imaginary part of a complex number 132
Implies 14
Improper convergence 178
inclusion 5
Inclusion, map 46
Inclusive or 10
Incomparable elements in an ordered set 76
Inconsistent postulate systems 62
Increasing sequence 161
Index set 48
Indexed direct product 53
Indexed intersection 51
Indexed union 51
Induced map, of a direct product 47
Induced map, of the power set 46
Induction, first principle 87
Induction, second principle 83 87
Induction, transfinite 83
Inductive definition of functions 89ff 144ff
Inductive proof 83 87
Inferior limits 175
Infimum 77
Infimum in  174
Infinite metric 224
Infinite products 212
Infinite series 191ff 182
Infinite set 141
infinity 173—175
Injective function 44
Integers 132
Interior, of a set 237
Interior, point 236
Intermediate-value theorem 281
Intersection, of a family of sets 51
Intersection, of two sets 29
Intervals 279
Intervals, connectedness 280
INTO 42
Intrinsic property of a configuration 57
Intuitionists 8
Inverse image, of a function 45
Inverse image, of a set 47
Isolated point 238
Isometric 224
Isomorphic 55
Isomorphism, of chains 85
Isomorphism, of configurations 55
Isomorphism, of ordered fields 105
Isomorphism, of ordered sets 73
Isomorphism, of simple chains 91
Isotone 73
Join of sets 30
Juxtaposition notation 30
Knaster fixed-point theorem 81
Lattice 78 Ex. 5
Laws of sines and cosines 338 Ex. 3
Least common extension of a family of functions 53 Ex.
Least subsystems 85—86
Least upper bound 77
Lebesgue convergence theorem 206
Lebesgue number of a covering 273 Ex. 15
Left-identity element 95
Left-zero element 95
Lemma 60
Length of a path 327
Lexicographic ordering 83 Ex. 3
Limit in 160ff
Limit in metric spaces 229ff
Limit, arithmetic combinations 168
Limit, definition 166 230
Lindeloef covering theorem 275
Linear order relation 75
List notation for sets 4 25
Local structure of analytic functions 334ff
Locally 272
Locally compact 272ff
Locally connected 282ff
Locally pathwise connected 284
Locally separable 277
Logarithm 319ff 215
Logarithm, principal branch 323
Logic 7ff
Logical connectives 8ff
Lower bound 77
m-adic rational 219
m-adic sequence 218
MAP 41 45
Map of ordered sets 73ff
Mapping 41
Mathematical induction 83 87
Mathematical logic 7
Maximal 76
Maximum 76
Maximum, condition 83
Maximum, point 315
Measure of a directed angle 331
Meet of sets 30
membership 3
Metric 223
Metric in  or  224—226
Metric, continuity of 244
Metric, infinite-valued 224
Metric, space 223ff
Metrizable space 251
Minimal 76
Minimum 76
Minimum, condition 83
Minimum, point 315
Model for a postulate system 62
Modular field 102
Modulus principle 315
modus ponens 19
Moebius function 196
Monomial function 244
Monotone 73
Monotone sequence 161
Moore — Smith theorem 256
Multiple-valued analytic function 323
Multiplication, of cardinals 156 157 159
Multiplication, of natural numbers 114
Multiplication, of positive real numbers 124
Multiplication, of rational numbers 119
Multiplication, of real numbers 126
n-sphere 226
Natural boundary of a function 315 Ex. 8
Natural map associated with an equivalence relation 66
Natural numbers 88—89 151 153
Natural projection in direct products 54
Necessary condition 14
Negative 104
Neighborhood of a point 238
Neutral element 95
Newton 332
Nondense set 239
NonNegative 104
Nonpositive 104
| Nonrectifiable path 327
NOT 9
Nowhere dense set 239
Null set 3
One-element set 4
One-to-one 45
Only if 14
Onto 42
Open covering 266
Open function 243
Open intervals 279
Open sets 235
Open subsets of 283
Operator 41
OR 9—10
Order in subsets 72
Order in the natural numbers 114
Order in the positive real numbers 122
Order in the rational numbers 119—120
Order in the real numbers 127
Order, of listing the members of a set 4
Order, relations 70ff
Order-preserving map 73
Order-reversing map 73
Ordered field 104ff
Ordered field, complete 108ff
Ordered pair 38
Ordered set 72
Ordered triples, etc. 38
Ordering a set 72
Ordinary induction 87
Parentheses 3
Partial order 75
Partial products 212
Partial sums 191
Partition of a set 66
Path 284
Path away from a point 335
Path, components of a space 284
Path, length of 327
Pathwise connected space 284
Peano 62
Peano's axioms for the natural numbers 89
Period 312 314
Periodic function 312
Periodic function, doubly 314 Ex. 7
Permanence of analytic identities 311
Placeholder 15 42
Point 223
Pointwise 199
Pointwise, convergence 247—248
Polar form of a complex number 331
Polynomial function 244
Positive 104
Positive integers 132
Positive real numbers 121ff
Postulates 59 153
Power series 239ff 210
Power set 37
Precompact space 272 Ex. 9
Prime subfield of a field 102
Principal branch of the logarithm 323
Principal value of the argument 330
Pringsheim's theorem 211 Ex. 14
Product, direct, of sets (old term) 29
Product, direct, of two sets 39
proof 19ff
Proper set inclusion 5—6
Proper subset 6
Proposition 61
Proposition in logic 8
Propositional function 15
Propositional scheme 15
Pseudometric 259 228
Ptolemy 332
Purely imaginary 132
Pythagoreans 121
Quantification 16
Quantified proposition with null domain 17
Quantifiers 16
Quaternary relation 50
Quaternion algebra 131 Ex. 3
Quotient map of an equivalence relation 66
Quotient set 66
Raabe's test 197 216
Radius of convergence of a power series 294
Radius of convergence of a power series, formula for 295
Range, of a function 41
Range, of a relation 50
ratio 121
Ratio, test 196 182
Rational function 244
Rational numbers 116ff 132
Real numbers 126ff
Real part of a complex number 132
Rectifiable path 327
Redundant postulates 61
Reflexive relation 65
Region of convergence of a power series 294
Regular function 298
Relation 49ff
Relative consistency 63
Remainder of a series after k terms 193
Representative of an equivalence class 66
Represents, power series represents a function 298
Repulsive fixed point 262
Restriction of a function 43—44
Riemann 196 338
Riemann hypothesis 196
Riemann sphere 178
Right-identity element 95
Right-zero element 95
Round-off 221
Rule of trichotomy 75
Russell's paradox 25 140 153 156
Schroeder — Bernstein theorem 138
Second element of an ordered pair 37
Segments of the integers 141
Self-contradictory postulate system 62
Semigroup 188
Separability of the space of continuous functions 276
Separable spaces 273ff
SEQUENCE 160
Set 1ff
Set, complements 34
Set, empty 3
Set, formation 24
Set, inclusion 5
Set, intersection of 29 51
Set, null 3
Set, union of 29 51
Set, universal 34
Set-theoretic paradoxes 25
Similarity of sets 136
Simple chain 88
Simple ordering 75
Sine, curve 285—286
Sine, function 310ff
Sine, Law of Sines 338 Ex. 3
Space, completeness 255
Space, metric 223ff
Space, of continuous functions 226 248 276
Space, separability 276
Space, topological 250
Sphere 226
Square roots in complete ordered fields 108—109
Standard English numerals 220
Standard m-adic representation of a number 219
Standard m-adic sequence 218
Steiner triple system 62
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