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Index Thierry VIALAR HANDBOOK OF MATHEMATICS Over a thousand Illustrations 2016 Index A-basis, 427 Additive associativity, 57, 700 A-module, 426 Additive category, 792 Ab-category, 792 Additive commutativity, 57, 700 Ab-enriched (symmetric) monoidal category, 792 Additive functor, 410, 808 Abel lemma, 163, 614 Additive group, 138 Abel theorem, 174 Additive group of integers modulo n, 117 Abel-Poisson, 661 Additive identity, 56, 57, 700 Abelian category, 791, 799 Additive inverse, 56, 57, 700 Abelian group, 56—58, 110, 114, 119, 120, 138, 643, Additive notation, 43, 52 645, 700, 701, 707, 791, 798, 810 additively and multiplicatively stable, 54 Abelian integral, 591, 592 Additively stable, 54 Abelian semigroup, 58, 701 Additivity axiom, 750 Abelian variety, 696 Adequate, 401 Abelianization, 426 Adequate subcomplex, 401 Abraham-Shaw, 1013 Adherent point, 265, 269, 297, 911 Absolute complement, 11, 15 Adherent point of a filter, 303 Absolute consistency, 6 Adic topology, 723, 771 Absolute extrema, 61 Adjective Absolute frequency, 839 autological, 18 Absolute geometry, 203, 206, 207 heterological, 18 Absolute gometry Adjoint, 820 models 1,2,3,4, 207 Adjoint endomorphism, 185 Absolute homology groups , 394 Adjoint functor, 408 Absolute Hurewicz theorem, 426 Adjoint functors, 805 Absolute maximum, 906 Adjoint functors (adjunction), 805 Absolute valuation, 106 Adjoint map, 331 Absolute value, 196, 440 Adjoint of a linear map, 331 in the field of rationals, 197 Adjoint operator, 331, 508 non-Archimedean, 197 Adjoint pair (of functors), 421 Absolute value of a rational number, 83 Adjointness, 797 Absolutely convergent series, 439 Adjunction, 805 Absolutely flat ring, 713 Adjunction isomorphism, 805 Absorbing, 43 Adjunction of indeterminates, 162 Absorbing element, 16, 44 Admissible open set, 414 Absorbing on the left, 44 Admissible parameter, 532 Absorbing on the right, 44 Admissible parameterization, 532 Absorbing state, 843 Affine algebraic set, 696 Absorption, 11, 12 Affine bijection, 230 Absorption laws, 16 Affine combination, 376 Abstract algebra, 357, 691 Affine connection, 565 Abstract algebraic variety, 696 Abstract category, 51, 808 Affine coordinates system, 259 Abstract Riemann surface, 585 Affine endomorphism, 260 Abstract simplicial complex, 399, 724 Affine form, 260 Abstract space, 501 Affine geometry, 211 Abstract variety, 696 Affine group, 229 Acceptance region, 835 Affine independent, 376 Accumulation point, 35, 266, 269 Affine independent set, 376 Action-angle variable, 939 Affine isometry, 255, 256 Acwise connectedness, 739 anti-displacement, 255 Acyclic carrier, 410 displacement, 255 Affine map, 229, 230 Acyclic complex, 392 3 Acyclic cover, 401 Affine map in R , 254 Acyclic cover of a simplicial complex, 401 Affine morphism, 764 Acyclic free chain complex, 409 Affine n-chain, 396 Acyclic free chain complex theorem, 409 Affine n-space, 366 Acyclic graph, 353 Affine neighborhood, 771 Acyclic model, 409 Affine orthogonal symmetry, 229 Acyclic object, 753, 754 Affine plane, 211 Acyclic resolution, 758 Affine plane of incidence, 211 Acyclic sheaf, 758 Affine scheme, 365, 697, 763, 766 Acyclic space, 389 Affine set, 376 Aczel’s constructive Zermelo-Fraenkel (CZF), 21 Affine set (convex set), 376 Addition and multiplication in N, 69 Affine space, 258, 376, 720 Addition in N, 69 affine subspace, 259 Addition in Q, 81 canonical structure, 259 Addition in Z, 78 vectorial structure, 259 Additive abelian group, 110 Affine space (algebraic geometry), 720 1054 Index Affine space (analytic geometry), 720 Algebraic topology, xix, 335, 366, 691 Affine subspace, 259 Algebraic variety, 357, 696, 697 Affine subspace intersection, 259 Algebraically closed, 104 Affine symmetry, 229 Algebraically closed field, 105, 152, 719, 771 Affine transformation, 230 Algebras for a monad, 803 Affine variety, 358, 696, 697, 720 Algebrization, 174 Affine Y-scheme, 764, 771 Almost everywhere convergence, 662 Affines map, 260 Alternating algebra, 185 Affinity, 229, 230 Alternating bilinear form, 608 Affix, 93, 95 Alternating form, 187 Afraimovich-Shilnikov theorem, 1001 Alternating group, 117, 187 Aggregate demand function, 915 Alternating map, 187 Agument predicate, 4 Alternating series, 439 AIC and SC criteria, 874 Alternative hypothesis H1, 835 AIC criteria, 875 Altitude, 227 AIC criterion, 855 Amalgamed sum, 818 AIC(p), 874 Ambient manifold, 737 Aitken estimator, 856 Amenable group, 24 Akaike criterion (AIC), 865 Amnestic functor, 805 Akaike function, 855 Ampère law, 493 Akaike information criterion, 855 Amplitude of cycle, 993 Akaike-Schwarz, 851 Amplitude spectrum, 894 Akaike-Schwarz criteria, 874 Analysis, xx, 435 Alembert theorem, 305 Analysis of autocorrelation function, 869 Aleph, 44 Analysis of residuals, 873 Aleph-0, 44, 46, 49 Analysis of shocks, 874 Aleph-1, 44, 47, 64 Analysis of variance, 834 Alexander-Veblen corollary, 400 Analysis of variance (ANOVA), 848 Alexander-Whitney theorem, 431 Analysis situs, xix Alexandroff compactification, 285 Analytic, 742 Alexandroff extension, 285 Analytic at, 742 Alexandroff theorem, 305 Analytic continuation, 570, 578, 597, 619 Algebra, xix, 109, 180, 358 Analytic continuations along different paths, 578 associative, 180 Analytic function, 451, 562, 577, 586, 742 commutative, 180 Analytic function at a point, 742 of Banach, 599 Analytic function on interior of domain, 742 σ-algebra (Σ-algebra, Ω-algebra), 693 Analytic functions, 569 Algebra of polynomials, 145 Analytic geometry, xix, 175, 204, 247 Algebra of sets, 11 real or complex, 204 Algebra of the disk, 623 Analytic manifold, 732 Algebraic basis, 332 Analytic representation, 234 Algebraic category, 802 Analytic set, 758 Algebraic closure, 92, 103, 166, 719 Analytic space, 758 Algebraic closure of a field, 92, 105 Analytic subspace, 758 Algebraic closure of C, 103 Analytic variety, 696 Algebraic complex numbers over Q, 157 Andronov-Hopf bifurcation, 995, 1013 Algebraic curve, 204, 455 Andronov-Hopf theorem, 995 Algebraic dimension, 289 Andronov-Pontryagin theorem, 979 Algebraic dual, 324 Andronov-Witt theorem, 973 Algebraic element, 719 Angle, 218, 222 Algebraic elements of a field, 164 acute, 218 Algebraic extension, 166 obtuse, 218 Algebraic extension of a field, 92, 719 of opening, 252 Algebraic function, 454, 591 reflex, 218 Algebraic fundamental group, 769 right, 218 Algebraic geometry, 692 straight, 218 Algebraic K-theory, 364, 761 Angle measure, 260 Algebraic number, 106, 157 Angle measure on a regular patch, 541 Algebraic number field, 106 Angle measurement, 219 Algebraic operation, 11, 693 Angle trisection, 102, 175 Algebraic operations in sets, 11 Angle-preserving transformation, 592 Algebraic point, 591 Annihilating element, 16 Algebraic problem, 174 Annulus, 266, 579, 605, 610, 629 Algebraic ramification, 585 Anosov, 953 Algebraic relation, 454, 455 Anosov automorphism, 950 Algebraic representation of a complex number, 94 Anosov diffeomorphism, 952, 953, 991 Algebraic set, 696 ANOVA equation, 848 Algebraic signature, 694 ANOVA table, 834 Algebraic space, 697 for simple regression model, 848 Algebraic structure, 50, 51, 109, 695, 697, 788 Antecedent, 40, 63, 467, 839 of integers, 85 Anti-adjoint, 331 of rationals, 86 Anti-matched lines, 208 of real numbers, 88 Anti-matching, 208 Algebraic structure of R, 435 Anti-matching theorem, 209 Algebraic surface, 204 Anti-paired lines, 208 Algebraic system, 359, 379, 692 Anti-self-adjoint operator, 331 1055 Index Antiautomorphism, 762 ARMA(p,q), 872 Anticonformal mapping, 592 ARMAX, 873 Antiderivative, 472, 473, 476, 479 Arnold, 928, 940 Antidual, 548 Arnold tongue, 1004, 1005 Antidual basis, 548 Arnold tongues, 1002 Antihomomorphism, 762 Arrangement, 829 Antilinear map, 328 Arrangements with repetitions, 831 Antinomy, 17 Arrangements without repetition, 831 semantic or syntactic, 17 Arrow, 779 Antipodal map, 397 Arrowsmith-Place, 957, 963 Antipode, 367, 397 Articulation vertex, 355 Antisymmetric function, 186 Artin braid group, 730 Antisymmetric map, 186 Artinian ring, 712 Antisymmetric multilinear form, 186 Artinian set, 47 Antisymmetrization, 187 Ascending chain condition (ACC), 709 Antisymmetrization operator, 186 Ascoli theorem, 320, 598 Antisymmetry, 10 Associate, 418 Aperiodic solution, 977 Associative law, 55 Apollonius circle, 228 Associative magma, 55, 699 Apollonius definition of a circle, 229 Associativity, 11, 12 Applied mathematics, xx Associativity isomorphism, 794 Approximation, 449 Associator, 793 Approximation by convolution, 667 Astroid, 455 Approximation by interpolation polynomial, 460 Asymptote, 453 Approximation by polynomials Asymptotic behavior of Fourier coefficients, 885 on a compact of Cn, 321 Asymptotic line, 545 on a compact of Rn, 321 Asymptotic point, 516 Approximation by trigonometric polynomials, 321 Asymptotic right triangle, 242 Approximation methods, 480 Asymptotical stability, 972 Approximation of vector functions, 321 Asymptotically stable, 929 Approximation theory, 458 Atlas, 559, 561, 734, 928 AR (autoregressive), 871 Atlas of class Cr (or Cr-atlas), 560 AR model, 871 Atom, 2, 13 AR(p), 857, 871 Atom of a lattice, 13 Arc, 267, 277 Atomic formula, 21 Arc length, 485 Attaching cell, 404 Arc length of curve, 485 Attaching map, 403, 404, 725 Arc length parameterization, 678 Attracting or repelling basin, 1012 Arc of a curve, 531 Attractor, 967, 980 ARCH (AR conditional heteroscedasticity), 861 Attractor in sense of Ruelle (1981), 992 ARCH model, 861 Attractor in the sense of Milnor, 967 ARCH test, 861 augmentation, 410 ARCH(q), 881 Augmentation homomorphism, 749 Archimedean property, 70, 90 Augmentation preserving, 410 Archimedean totally ordered
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