Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Simmons G.F. — Introduction to topology and modern analysis
Simmons G.F. — Introduction to topology and modern analysis

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Introduction to topology and modern analysis

Автор: Simmons G.F.

Аннотация:

This material is intended to contribute to a wider appreciation of the mathematical words "continuity and linearity". The book's purpose is to illuminate the meanings of these words and their relation to each other.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 372

Добавлена в каталог: 03.03.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$L_{p}$ space      215
$\epsilon$-net      123
Absolute value, of a function      159
Absolute value, on complex plane      53
Absolute value, on real line      52
Achieser, N.I.      157
Adjoint operation (involution), on $\mathcal{B}(H)$      265
Adjoint operation (involution), on Banach *-algebra      324
Adjoint, of element in Banach *-algebra      324
Adjoint, of operator      263
Alexandroff, P.      130n
Algebra      106 208
Algebra B*      324
Algebra Banach      302
Algebra Banach*      324
Algebra Boolean      see “Boolean algebra”
Algebra center      210
Algebra commutative      106
Algebra complex      106
Algebra disc      303
Algebra division      208
Algebra group      303—305
Algebra homomorphism      210
Algebra ideal in      209 313
Algebra isomorphism      210
Algebra quotient algebra of      209
Algebra radical      314
Algebra regular representation      210
Algebra semi-simple      316
Algebra subalgebra of      106 208
Algebra total matrix      284
Algebra von Neumann      303
Algebra W*-      303
Algebra with identity      106
Antisymmetry      43
Arzela's theorem      123
Ascoli's theorem      126 128
Axiom of Choice      46
B*-algebra      324
B*-algebra representation      325—326
Baire's theorem      74 75n
Banach *-algebra      324
Banach *-algebra, *-isomorphism      324
Banach algebra      302
Banach algebra, Banach subalgebra of      302
Banach algebra, representation      305
Banach space      82 212
Banach space, closed unit sphere      217 232
Banach space, representation      234
Banach space, uniformly convex      248
Banach — Steinhaus theorem      240
Banach — Stone Theorem      330
Bar-Hillel, Y.      7 46n
Base, closed      112
Base, generated by subbase      101 112
Base, open      99
Basis      197
Basis, orthonormal      293
Bell, E.T.      37
Bernstein polynomials      154
Bers, L.      338
Bessel's inequality      252—253 257
Birkhoff, G.      29 46n 47
Birkhoff, G.D.      338
Bolzano — Weierstrass property      21
Bolzano — Weierstrass theorem      121
Boolean algebra      345
Boolean algebra as Boolean ring      347—349
Boolean algebra, isomorphism      353
Boolean algebra, of sets      12 344
Boolean algebra, representation      353
Boolean ring      346
Boolean ring as Boolean algebra      348—349
Boolean ring as field      349—350
Boolean ring, maximal ideals in      350
Boolean ring, representation      351
Boolean ring, semi-simplicity      350
Boundary      68 97
Boundary point      68 97
Bounded function      55
Bounded linear transformation      220
Bounded mapping      58
Bounded set      58
Brouwer's fixed point theorem      338
C*-algebra      303
C*-algebra, commutative      332—334
Canonical form problem for matrices      286
Cantor continuum hypothesis      39
Cantor intersection theorem      73
Cantor set      67
Cantor, G.      31—43 49
Cardinal number(s)      31
Cardinal number(s) comparability theorem      48
Cardinal number(s) finite      32
Cardinal number(s) of continuum      39
Cartesian product (product of sets)      23—25
Cauchy sequence      71
Cauchy's inequality      88 219
Cayley's theorem      181
Chain      44
Characteristic equation      288-289
Characteristic value      278n
Characteristic vector      278n
Choice, axiom of      46
class      4
Class disjoint      9
Clelfand representation theorem      322
Closed base      112
Closed base, generated by closed subbase      112
Closed graph theorem      238
Closed mapping      342
Closed rectangle      101 119
Closed set      65 95
Closed sphere      66
Closed strips      101
Closed subbase      112
Closed unit sphere      217 232
Closure      58
Compact subspace      111
Compact topological space      110 111
Compactification, one-point      163
Compactification, Stone — Cech      141 331
Comparability theorem for cardinal numbers      48
Comparable elements      7 44
Complete metric space      71
Complete orthonormal set      255
Completely regular space      133
Completion of metric space      84—85
Complex plane      23 52—54
Complex plane extended      162
Component of a space      146
Congruent modulo, a linear subspace      193
Congruent modulo, a positive integer      30
Congruent modulo, an ideal      186
Conjugate space      224
Conjugate, of a function      108 161
Conjugate, of operator      241
Connected space      142 143
Connected subspace      143
continuous curve      341—342
Continuous function      50
Continuous image      93
Continuous linear functional      224
Continuous linear transformation      219 220
Continuous mapping      76 93
Continuous mapping at point      75-76 104
Continuous mapping in single variable      118
Continuous mapping jointly      118
Continuum, cardinal number      39
Continuum, hypothesis      39
Contraction      338
Convergence of functions, point wise      83
Convergence of functions, uniform      83
Convergent sequence, in a space      70 132
Convergent sequence, limit      50 71 132
Convergent sequence, of numbers      50
Convex set      148
Convolution      304—305
Coordinate plane      22
cosets      186—187 193—194
Countably compact space      114
Courant, R.      94 338
Curve, continuous      341—342
Dense (everywhere dense) set      70 96
Derived set      96
Determinant, of matrix      287
Determinant, of operator      288
Dimension orthogonal, of a Hilbert space      259—260
Dimension, of a linear space      200
Disc algebra      303
Disconnected space      143
Disconnection of a space      143
Discrete space      93
Discrete topology      93
Discrete two-point space      144
Disjoint linear subspaces      195
Disjoint sets      9
Distance between two points      51
Distance, from point to set      58
Distributive laws, for lattices      345
Distributive laws, for sets      10
Division algebra      208
Divisor of zero      183
Divisor of zero topological      307
Dixmier, J.      303n
Dunford, N.      ix 226 232n
Eigenspace      278
Eigenvalue      278
Eigenvector      278
Element(s)      3
Element(s) comparable      7 44
Element(s) in ring, regular      183 314
Element(s) in ring, singular      183 314
Element(s) maximal      44
Empty set      5
Equicontinuous functions      126
Equivalence relation      27
Equivalence set      27
Euclidean plane      22 87—88
Euclidean space, infinite-dimensional      90
Euclidean space, n-dimensional      24 87 214
Everywhere dense set      70 96
Extended complex plane      162
Extended real number system      56
Family      4
Field      184
Finite intersection property      47 112
First countable space      100n
Fixed point      338
Fixed point space      337—338
Fixed point theorem, Brouwer's      338
Fixed point theorem, Schauder's      338
Fomin, S.V.      128 215n
Fourier coefficients      256 257
Fourier expansion      256 257
Fraenkel, A.A.      7 42n 46n
Full linear group      207
Function spaces      82
Function(s), absolute value      159
Function(s), bounded      55
Function(s), complex      17
Function(s), conjugate      108 161
Function(s), constant      16
Function(s), continuous      50
Function(s), continuous at point      50
Function(s), convergence, pointwise      83
Function(s), convergence, uniform      83
Function(s), definition      16
Function(s), domain      15 16
Function(s), equicontinuous      126
Function(s), extension      17
Function(s), generalities      14—16
Function(s), imaginary part      161
Function(s), in contrast to mapping      17
Function(s), moments      157
Function(s), range      15 16
Function(s), real      17
Function(s), real part      161
Function(s), restriction      17
Function(s), uniformly bounded      see also “Mapping” 128n
Function(s), vanishing at infinity      165
Functional(s)      224
Functional(s) extension      226—228
Functional(s) induced      231
Functional(s) multiplicative      321
Functional(s) on Hilbert space, representation      261
Fundamental theorem of algebra      245 289 310
Gal, I.S.      240
Galileo      33
Gelfand mapping      319
Gelfand — Neumark theorems      318 325—326
Godol, K.      39n
Goffman, C.      128
Goldberg, R.R.      305n
Gram — Schmidt process      258 295
Graph of mapping      23
Group      172—173
Group Abelian (commutative)      173 179
Group Abelian (commutative) additive      179
Group algebra      303—305
Group, abstract vs. concrete      173n
Group, center of      180
Group, circle      174
Group, finite      173
Group, full linear      207
Group, homomorphism      180
Group, identity in      173 179
Group, infinite      173
Group, inverses      173 179
Group, isomorphic      180
Group, isomorphism      180
Group, of symmetries of square      176—177
Group, order      173
Group, permutation      17
Group, regular representation      181
Group, subgroup of      178
Group, symmetric      176
Group, transformation      178 181
Hahn — Banach theorem      21 228
Hahn — Banach theorem, generalized form      230—231
Hahn — Mazurkiewicz Theorem      343
Hahn, H.      343
Halmos, P.R.      42n 46n 172 215n
Hausdorff space      130
Heine — Borel theorem      110 114
Heine — Borel theorem converse      115
Heine — Borel theorem generalized      119
Hermifce functions      259
Hewitt, E.      121n
Hilbert cube      248
Hilbert space(s)      245
Hilbert space(s) among complex Banach spaces      248
Hilbert space(s) inner product      245
Hilbert space(s) orthogonal complements      249
Hilbert space(s) orthogonal dimension      259—260
Hilbert space(s) orthogonal subspaces      250
Hilbert space(s) orthogonal vectors      249
Hilbert space(s) orthonormal set      251
Hilbert space(s) orthonormal set complete      255
Hilbert space(s) parallelogram law      247
1 2 3
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте