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Howes N.R — Modern Analysis and Topology
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: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Star refinement      8
Stone — Cech compactification      70 157
Stone, A.H.      7 10
Stone, M.H.      157 159
Stone’s theorem      6 17
Strictly coarser      92
Strictly finer      92
Strictly isogeneous      281
Strongly inaccessible cardinal      226
Strongly stable covering      169
Sub-base      47
Sub-basis      44
Subadditive      238 239
Subbase      208
Subcategory      151
Subcategory, full      151
Subfine      139
Subfine coreflection      139 142
Subgroup, normal      273
Subnet      86
Subtractive set function      235
Sufficiently small      289
Sum of transfinite sequences      79
Supercomplete      110
Supercompletion      191
Support      5
Supremum norm      176 325
Supremum topology      111
Supremum uniformity      111
Supremum, essential      319
Symmetric entourage      46
Symmetric set      272
Tamano — Morita paracompactification      158 182 197 200
Tamano, H.      103 156 160 166 170 171 174 175 177 180 217 218 220
Tamano’s Completeness Theorem      160 171
Tamano’s Theorem      160 171 178
Topological completion      103 156
Topological group      271
Topologically complete      175
Topologically preparacompact      188
Topology assoc, with a uniformity      45
Topology of compact convergence      364
Topology of uniform convergence      360
Topology, point-wise convergence      355
Total variation      371
Totally bounded      94
Transfinite sequence      62
Transfinite subsequence      63
Translation      266
Translation invariance      263 264
Triangle inequality      1
Trigonometric polynomial      339
Trigonometric system      338
Tukey, J.W.      7 13 43 56 59 60 61 83
u-uniformity      66
uc topology      360
uc uniformity      360
Uniform boundedness principle      351
Uniform boundedness theorem      347 351
Uniform compactification      154
Uniform convergence      27
Uniform convergence on compacta      364
Uniform covering      44
Uniform derivative      376 389
Uniform function space      355
Uniform homeomorphism      26 48
Uniform imbedding      150
Uniform local compactness      95 96 118 133
Uniform paracompactification      103 158
Uniform paracompactness      83 92
Uniform product space      114
Uniform property      26
Uniform quotient      115 118
Uniform relation      118
Uniform retract      146
Uniform space      44
Uniform space, equi-homogeneous      267
Uniform space, injective      139
Uniform space, isogeneous      266
Uniform structure      43
Uniform sum      117
Uniform topology      45
Uniformities, family of      54
Uniformity      43
Uniformity of uniform convergence      359
Uniformity, bounded continuous function      53
Uniformity, continuous function      53
Uniformity, derivative      134
Uniformity, derived      104
Uniformity, e      67
Uniformity, entourage      46
Uniformity, induced      99
Uniformity, inductive limit      113
Uniformity, infimum      111
Uniformity, k      364
Uniformity, left      276
Uniformity, metric      56
Uniformity, non-separating      44
Uniformity, point finite      144
Uniformity, point-wise convergence      355
Uniformity, product      355
Uniformity, projective limit      113
Uniformity, pseudo-metric      208
Uniformity, relativized      99
Uniformity, right      276
Uniformity, supremum      111
Uniformity, u      66
Uniformity, uniformity $\beta$      70
Uniformity, universal      55
Uniformity, weak      52
Uniformizable      52
Uniformly continuous      26 48 51
Uniformly differentiable      390
Uniformly discrete      133
Uniformly locally uniform      133
Uniformly paracompact      95
Uniformly separated      288
Uniformly strict shrinking      52
Universal net      89
Universal uniformity      55
Upper semi-continuous      258
Urysohn Metrization Theorem      14 16
Urysohn, P.      8 14 16 73
Urysohn’s imbedding theorem      16
Urysohn’s lemma      16
Vanish at infinity      325
Variation, negative      373
Variation, positive      373
Vietoris, L.      119
von Neumann, J.      264 305
Weak completion      129
Weak topology      353
Weak uniformity      52
Weakly Cauchy filter      102
Weakly complete      129
Weak^{*} topology      353 369
Weil, A.      43 264 266
Well ordered covering      65
Within      45
Z(f)      162
Zero set      162
Zero-boundary      289
Zero-one measure      221
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