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Howes N.R — Modern Analysis and Topology

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Название: Modern Analysis and Topology

Автор: Howes N.R

Аннотация:

The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. The reader should have taken an advanced calculus course and an introductory topology course. It is intended that a subset of the book could be used for an upper-level undergraduate course whereas much of the full text would be suitable for a one-year graduate class. An attempt has been made to document the history of all the central ideas and references and historical notes are embedded in the text. These can lead the interested reader to the foundational sources where these ideas emerged.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 472

Добавлена в каталог: 11.12.2011

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Предметный указатель

$C^{*}$ -imbedded      184
$C^{*}(X)$       3
      266
$C_\infty(X)$       325
$I(\omega)$       15 20
$I^\omega$       $67
-differentiable measure      390
      334
$L^2(\mu)$       326
$L^p(\mu)$       340
$l_\infty$ -space      141
$\beta$ -uniformity      70
$\Delta$ -refinement      8
$\mathcal{U}$ -close      119
$\mathcal{U}$ -large      95
$\mathcal{U}$ -small      95
$\mu^{*}$ -measurable      239
$\omega$ -directed      104
$\sigma$ -additive      231
$\sigma$ -algebra      230
$\sigma$ -compact      168
$\sigma$ -locally finite      17
$\sigma$ -ring      230
0(f)      162
Abelian group      273
Absolute continuity      372
Absolutely closed      42
Abstract category      147
Accumulation point, complete      74
Additive set function      235
Alexandrov, P.      73
Algebra      230
Algebra, measure      231
Almost Cauchy      121
Almost everywhere (a.e.)      256
Almost paracompact      189
Almost regular      260
Almost regular measure      387
Almost uniform measure      306
Almost-2-fully normal      73 108
Arhangel'skii      19
Arhangel'skii's Metrization Theorem      19
Ascending collection      63
Ascoli theorem      368
Axiom of Choice      77
Baire measure      233
Baire set      231
Baire, R.      347
Ball      45
Banach space      340
Banach space isomorphism      347
Banach — Steinhaus theorem      352
Banach, S.      340
Base      47 208
Basis      44
Basis of a vector space      332
Basis, isomorphic      266
Bessel’s inequality      334
Birkhoff, G.      83
Bonding map      126
Borel compact      35 37
Borel field      304 305
Borel function      245
Borel measure      233
Borel set      231
Bounded      21
Bounded collection      96
Bounded continuous function uniformity      53
Bounded function      3
Bounded linear transformation      341
Bounded open set      310
Bounded, essentially      319
Bourbaki      43 83 119
Burdick, B.      121 122 139 191 192
C(X)      266
C-complete      97
C-imbedded      184
Canonical injection      117
Caratheodory, C.      238
Cardinal, inaccessible      226
Cardinal, strongly inaccessible      226
Categorical definition      149
Categorical property      147
Category      146
Category isomorphism      147
Category, abstract      147
Category, concrete      147
Cauchy      29 90
Cauchy filter      102
Cauchy, almost      121
Cauchy, partially      136
Cech, E.      157 159 165
Chain, increasing      295
Characteristic function      222
class      147
Closed class of cardinals      224
Closed function      82
Closed graph theorem      347
Closed sphere      6
Closed vector subspace      328
Cluster      29 63 85
Cluster class      80
Cluster point      29 120
Coarser      44 92
Cofinal      29 63 84
Cofinal completeness      28 92
Cofinal completion      103
Cofinal function      86
Cofinally $\Delta$ -Cauchy      73 108
Cofinally $\Delta$ -complete      108
Cofinally Cauchy      29 91
Cofinally complete      30 93
Collectionwise normal      21 25
Compact      31
Compact-open topology      364
Compactification      156
Compactification, Stone — Cech      157
Comparable filters      92
Compatible function      97
complete      30 93
Complete accumulation point      74
Complete measure      231
Complete, topologically      175
Completely additive      305
Completely normal      20 25
Completeness      92 28
Completion      38 97
Completion of a measure      232
Completion, topological      103
Complex measure      370
Composition of entourages      46
Concentrated      372
Concrete category      147
Conjugate exponent      318
Contained in a net      97
Content, Jordan      305
Content, Loomis      288
Continuous from above      237
Continuous from below      237
Continuous function      3
Continuous function uniformity      53
Continuous in metric topology      4
Contravariant functor      148
Converge      29 63 85
Converge uniformly      27
Converge weakly      352
Convergence class      89
Convex function      317
Convex vector space      328
Coordinate space      114

Coreflection      153
Coreflection functor      153
Corson, H.      102
Coset, left      276
Coset, right      276
Countably bounded      104
Countably compact      23
Countably directed      104
Countably metacompact      63
Countably paracompact      63
Countably subadditive      238
Counting measure      334
Covariant functor      147
Covering uniformity      43
Covering, residue      108
Covering, strongly stable      169
CZ-maximal      203
Decomposition, Jordan      373 380
Decomposition, Lebesgue      380 381
Decomposition, polar      380 382
Dense with respect to <      288
Derivative uniformity      134
Derived uniformity      104
Descending collection      63
Diameter      21
Dieudonne, J.      7 8 163
Differentiable measure      389
Directed collection      109
Directed ordering      84
Directed, countably      104
Discrete      20
Distance      5
Distance between sets      5
Distance from a point to a set      5
Distance function      1
Distance, Hausdorff      125
Distinguish points      15
Distinguish points from closed sets      15
Dominate      371
Dot product      326
Dowker, C.H.      63
Dual operator      352
Dual space      343 352 376
Dual space, second      346
Duality      149
Duality principle      150
E-complete      203
e-uniformity      67
Entirely normal      108
Entourage      46
Entourage uniformity      46
Entourage, symmetric      46
Epimorphism      148
Equi-continuity      267
Equi-homogeneous uniform space      2
Equicontinuous      366
Equivalent pseudo-metrics      5
Essential supremum      319
Essentially bounded      319
Eventually      29 63 85
Exponent, conjugate      318
Extension of a measure      239
Extension of a set      160
Extension, proper      161 162
Family of uniformities      54
Fee measure      224
Filter      83 91
Filter, assoc. with a net      91
Filter, Cauchy      102
Filter, intersection      91
Filter, neighborhood      91
Finally compact      74
Fine      55
Fine space      55
Finer      92 44
Finite measure      234
First category      348
Fourier coefficients      353
Fourier series      353
Frequently      29 63 85
Fubini’s Theorem      392
Full subcategory      151
Fully normal      8
Function, Borel      245
Function, characteristic      222
Function, convex      317
Function, Haar      292
Function, Harr covering      292
Function, linear      257
Function, measurable      243
Function, nonexpansive      267
Function, perfect      182
Function, quasi-perfect      197
Function, simple      246
Function, simple measurable      247
Functionally separated      180
functor      146
Functor, contravariant      148
Functor, coreflection      153
Functor, covariant      147
Functor, reflection      152
Fundamental basis      97
Fundamental net      97
Generate      45 208
GENERATED      92
Gillman, L.      203
Ginsburg, S.      110 118 133 134 154
Glicksberg, I.      176
Group, topological      271
Haar covering function      292
Haar function      292
Haar integral      266
Haar measure      266
Haar, A.      264
Hahn decomposition theorem      380 385
Hahn — Banach theorem      344 347
Halmos, P.      260
Hausdorff distance      125
Hausdorff uniformity      43
Hausdorff, F.      119 347
Heavily bounded      96
Heavy collection      96
Hedgehog space      97
Hereditarily open prering      288
Hereditarily realcompact      216
Hereditary collection      238
Hewitt realcompactification      157 203
Hewitt, E.      204
Hilbert cube      15 16 20
Hilbert space      4 25 34 326 327 338
Hilbert space isomorphism      337
Hilbert, D.      326
Hoelder’s inequality      318 319
Hohti, A.      96 181 182
Homogeneous topological space      266
Howes, N.      66 70 72 75 76 93 102 104 188 189 191 192 219 278 390
Hyperfunction      125
Hyperspace      119
Imbedding morphism      151
Imbedding, uniform      150
Inaccessible cardinal      226
Increasing chain      295
Indefinite integral      391
Induced uniformity      99
Inductive limit topology      113
Inductive limit uniformity      113
Infimum topology      111
Infimum uniformity      111
Infinite measure      234
Injective uniform space      139

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