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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
Inner product      326
Inner product space      326
Inner regular      260
Instance      147
Integral, Haar      266
Integral, Lebesgue      249
Intersection filter      91
Interval of indicies      299
Invariance, translation      263
Invariant Loomis content      289
Invariant on compact spheres      300
Inverse image of a covering      48
Inverse limit sequence      126 128
Inverse limit space      126 128
Isbell, J.R.      43 61 110 111 118 124 133 134 137 145 154 188 221
Ishikawa, F.      63 64
Isogeneous, perfectly      281
Isogeneous, strictly      281
Isogeneous, uniform space      266
Isometric function      27
Isometrically imbedded      38
Isomorphic basis      266
Isomorphism      26 266
Isomorphism, Banach space      347
Isomorphism, category      147
Isomorphism, Hilbert space      337
Iterated limit      89
Itzkowitz, G.      264 265 269
Jerison, M.      203
Joint continuity      362
Joint continuity on compacta      364
Jointly continuous      362
Jordan content      305 306
Jordan decomposition      373 380
Jump      295
k-bounded      191
Kakutani, S.      260
Kasahara      32
Katetov, M.      7
Kernel      340
Kodaira, K.      265 305
Lebesgue covering theorem      22
Lebesgue decomposition      380 381
Lebesgue integrable      255
Lebesgue integral      249
Lebesgue measure      233 262
Lebesgue number      22
Lebesgue property      31 93
Lebesgue ring      234
Lebesgue, H.      251 254
Left coset      276
Left uniformity      276
Lexicographic ordering      79
Limit of a monotone sequence      314
Limit uniformity      111
Limit, inferior      245 248
Limit, inferior of a net      125
Limit, iterated      89
Limit, point-wise      246
Limit, superior      245 249
Limit, superior of a net      125
Lindeloef, E.      69 70
Lindeloef, linearly      74
linear combination      331
Linear function      340
Linear functional      257 340
Linear functional, real      343
Linear operator      340
Linear transformation      340
Linear transformation, bounded      341
Linearly independent      331
Linearly Lindeloef      74
Locally fine      133
Locally fine coreflection      133
Locally finite      5 8
Locally starring      19
Loomis content      288
Loomis, L.      284 285 297 299 305 306
Lower semi-continuous      258
Lusin’s theorem      323
M-additive measure      224
M-paracompact      65
M-space      103 197
Mack, J.      65 186
Mansfield      73
Measurable cardinal      221 222
Measurable function      243
Measurable set      243
Measurable space      243
Measure      231
Measure algebra      231
Measure ring      231
Measure, $L^1$-differentiable      390
Measure, almost regular      387
Measure, almost uniform      306
Measure, Baire      233
Measure, Borel      233
Measure, complete      231
Measure, complex      370
Measure, counting      334
Measure, differentiable      389
Measure, extension of      239
Measure, finite      234
Measure, free      224
Measure, Haar      266
Measure, infinite      234
Measure, Lebesgue      233 262
Measure, M-additive      224
Measure, outer      239
Measure, regular      387
Measure, regular complex      373
Measure, zero-one      221
Metric      2
Metric assoc. with a pseudo-metric      27
Metric property      26
Metric space      2
Metric uniformity      56
Metric, discrete      2
Metric, trivial      2
Metrization problem      13
Mibu, Y.      264 265
Michael, E.      65
Minkowski’s inequality      318 319
Miscenko      74
Monomorphism      148
Monotone class      314
Monotone decreasing      91
Monotone increasing      91
Monotone sequence      314
Monotone set function      235
Moore, E.H.      83
Morita, K.      7 43 58 59 60 69 103 129 131 132 156 163 165 194 196 197 198
Morphism      147
Morphism function      147
Morphism, imbedding      151
Morphism, quotient      151
Morphism, reflection      151
Nachbin, L.      265
Nagata — Smirnov metrization theorem      14 16 17
Nagata, J.      7 16
Negative part of a function      246
Negative variation      373
Negligible set      256
Neighborhood filter      91
Neighborhood principle      75
Net      83 84
Net, universal      89
Nikodym, O.      374
Non-separating uniformity      44
Nonexpansive function      267
Norm      341
Norm quotient      353
Norm supremum      325
Norm topology      340
Normal covering      13 55 56
Normal family      44
Normal in      45
Normal sequence      13 44
Normal subgroup      273
Normal with respect to      45
Normal, entirely      108
Normalized      332
Normed linear space      340
Nowhere dense      348
Object      147
Object function      147
open      2
Open function      82
Open mapping theorem      347 349
Operator, dual      352
Ordering lemma      75
Ordering, directed      84
Ordering, lexicographic      79
Ordering, product      88
Orthogonal ($\perp$)      328 332
Orthogonal measures      372
Orthogonal projection      330
Outer measure      239
Outer regular      260
Paracompact      8
Paracompactification      156
Paracompactification, uniform      158
Partial convergence      136
Partial net      136
Partially Cauchy      136
Partition      370
Partition of unity      5
Partition of unity subordinate to a covering      5
Pasynkov, B.      132
Pelant, J.      74 139 145 154
Perfect mapping      182
Perfectly isogeneous      281
Perfectly normal      20 25
Phalanxes      83
Point finite      9
Point finite uniformity      144
Point-wise limit      246
Points at infinity      178 179
Polar decomposition      380 382
Positive part of a function      246
Positive variation      373
Precise refinement      57
Precompact      22 94
Precompact reflection      154
Preparacompact      103
Prering      288
Prering, hereditarily open      288
Preuniformity      44
Product ($\pi$) topology      355 369
Product of objects      149
Product ordering      88
Product uniformity      355
Projective limit space      112
Projective limit uniformity      113
Proper extension of a covering      162
Proper extension of a set      161
Proper net      121
Pseudo-compact      201
Pseudo-metric      1
Pseudo-metric space      2
Pseudo-metric uniformity      208
Pseudo-paracompact      201
q-space      203
Quasi-perfect function      197
Quotient function      82
Quotient morphism      151
Quotient norm      353
Quotient normed linear space      353
Quotient of a topological group      276
Quotient topological group      277
Quotient uniform space      115
Quotient, uniform      115 118
Radical      171
Radon — Nikodym derivative      370 373 374
Radon, J.      374
Realcompact      203
Realcompact, hereditarily      216
Realcompactification      210
Realcompactification, Hewitt      157 203
refinement      7
Refinement, precise      57
Reflection      151 266
Reflection functor      152
Reflection morphism      151
Reflection, precompact      154
Reflexive normed linear space      347
Regular      260
Regular complex measure      373
Regular measure      387
Regular, almost      260
Regular, inner      260
Regular, outer      260
Regularly bounded      35 37
Regularly open      54 171
Relatively fine spaces      75
Relativized uniformity      99
Residual      63 84 136
Residue covering      108
Residue point      108
Retract, uniform      146
Retraction      146 148
Rice, M.      95 96
Riesz representation theorem      260 261 387
Riesz — Fischer theorem      335
Riesz, F.      257 260
Right coset      276
Right uniformity      276
Ring      3 230
Ring, Lebesgue      234
Ring, measure      231
Rotation      266
Rudin, M.      74
Russell paradox      147
Samuel compactification      154 157
Samuel, P.      157
Scalar product      326
Schwarz inequality      327
Second category      348
Second dual space      346
Segal, I.      264 265
Separable reflection      154
Separated, uniformly      288
Sequentially compact      23
Set at infinity      179
Shirota, T.      43 67 204 211 221 227
Shirota’s Theorem      221
shrink      9
Shrinkable      9
Shrinking, uniformly strict      52
Simple function      246
Simple measurable function      247
Small, sufficiently      289
Smirnov, Y.M.      7 16 17
Smith, H.L.      83
span      331
Spectrum of $\beta X$      192
Sphere      2 45
Square integrable      326
Star      7 8
Star finite      57
1 2 3
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