Hyperspaces: fundamentals and recent advances
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1999
|
| Schriftenreihe: | Pure and applied mathematics
216 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 512 S. graph. Darst. |
| ISBN: | 0824719824 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804126962257494017 |
|---|---|
| adam_text | HYPERSPACES FUNDAMENTALS AND RECENT ADVANCES ALEJANDRO 11 LANES
UNIVERSIDAD NACIONAL AUTONOMA DE MEXICO CIUDAD UNIVERSITARIA, MEXICO SAM
B. NADLER, JR. WEST VIRGINIA UNIVERSITY MORGANTOWN, WEST VIRGINIA M A R
C E L MARCEL DEKKER, INC. NEW YORK * BASEL CONTENTS PREFACE V PART ONE
I. THE TOPOLOGY FOR HYPERSPACES 3 1. THE GENERAL NOTION OF A HYPERSPACE
3 TOPOLOGICAL INVARIANCE 5 SPECIFIED HYPERSPACES 6 EXERCISES 7 2. THE
HAUSDORFF METRIC H D 9 PROOF THAT H D IS A METRIC 11 A RESULT ABOUT
METRIZABILITY OF CL(X) 12 EXERCISES 14 3. METRIZABILITY OF HYPERSPACES
16 METRIZABILITY OF 2 X 16 METRIZABILITY AND COMPACTNESS OF CL(X) 18
EXERCISES 19 4. CONVERGENCE IN HYPERSPACES 20 L-CONVERGENCE,
TY-CONVERGENCE 20 RELATIONSHIPS BETWEEN L-CONVERGENCE AND
TY-CONVERGENECE . 22 WHEN X IS COMPACT HAUSDORFF 25 COUNTABLE
COMPACTNESS IS NECESSARY 26 EXERCISES 26 REFERENCES 28 IX X TABLE OF
CONTENTS II. EXAMPLES: GEOMETRIC MODELS FOR HYPERSPACES 31 5. C(X) FOR
CERTAIN FINITE GRAPHS X 33 X AN ARC 33 X A SIMPLE CLOSED CURVE 35 X A
NOOSE 36 X A SIMPLE N-OD 39 HISTORICAL COMMENTS . . 44 EXERCISES 44 6.
C(X) WHEN X IS THE HAIRY POINT 46 EXERCISES 50 7. C(X) WHEN X IS THE
CIRCLE-WITH-A-SPIRAL 51 CONES, GEOMETRIC CONES 51 THE MODEL FOR C(X) 53
KNASTER S QUESTION 59 WHEN C(Y) CONE(Y) 59 EXERCISES 62 8. 2 X WHEN X
IS ANY COUNTABLY INFINITE COMPACTUM 64 CANTOR SETS 65 PRELIMINARY
RESULTS 65 STRUCTURE THEOREM 67 UNIQUENESS OF COMPACTIFICATIONS 67 THE
MODEL FOR 2 X 70 EXERCISES 72 REFERENCES 72 III. 2 X AND C(X) FOR PEANO
CONTINUA X 75 9. PRELIMINARIES: ABSOLUTE RETRACTS, Z-SETS, TORURICZYK S
THEOREM 76 EXERCISES 79 10. PRELIMINARIES: GENERAL RESULTS ABOUT PEANO
CONTINUA . . . . 80 EXERCISES 83 11. THE CURTIS-SCHORI THEOREM FOR 2 X
AND C(X) 85 WHEN 2G AND C K (X) ARE Z-SETS 85 THE CURTIS-SCHORI THEOREM
89 FURTHER USES OF TORURICZYK S THEOREM 90 EXERCISES 91 REFERENCES 94
TABLE OF CONTENTS XI IV. ARCS IN HYPERSPACES 97 12. PRELIMINARIES:
SEPARATION, QUASICOMPONENTS, BOUNDARY BUMPING 97 EXERCISES - 103 13. A
BRIEF INTRODUCTION TO WHITNEY MAPS 105 DEFINITION OF A WHITNEY MAP 105
EXISTENCE OF WHITNEY MAPS 106 EXERCISES 108 14. ORDER ARCS AND ARCWISE
CONNECTEDNESS OF 2 X AND C(X) . . . 110 DEFINITION OF ORDER ARC 110
ARCWISE CONNECTEDNESS OF 2 X AND C(X) 110 APPLICATION: 2 X D I 114
ORIGINAL SOURCES 116 EXERCISES 117 15. EXISTENCE OF AN ORDER ARC FROM AO
TO AI 119 NECESSARY AND SUFFICIENT CONDITION 119 APPLICATION:
HOMOGENEOUS HYPERSPACES 122 ORIGINAL SOURCES 124 EXERCISES 124 16.
KELLEY S SEGMENTS 127 KELLEY S NOTION OF A SEGMENT 127 RESULTS ABOUT
SEGMENTS 128 ADDENDUM: EXTENDING WHITNEY MAPS 131 ORIGINAL SOURCES 132
EXERCISES 132 17. SPACES OF SEGMENTS, S W (K) 134 COMPACTNESS 134 S W
(?0 *SO{H) 136 S W (2 X ),S W (C(X)) WHEN X IS A PEANO CONTINUUM 138
APPLICATION: MAPPING THE CANTOR FAN ONTO 2 X AND C(X) . . 140 ORIGINAL
SOURCES 141 EXERCISES 141 XII TABLE OF CONTENTS 18. WHEN C(X) IS
UNIQUELY ARCWISE CONNECTED 143 STRUCTURE OF ARCS IN C(X) WHEN X IS
HEREDITARILY INDECOMPOSABLE 145 UNIQUENESS OF ARCS IN C(X) WHEN X IS
HEREDITARILY INDECOMPOSABLE 146 THE CHARACTERIZATION THEOREM 148
ORIGINAL SOURCES 148 EXERCISES 148 REFERENCES 149 V. SHAPE AND
CONTRACTIBILITY OF HYPERSPACES 153 19. 2 X AND C(X) AS NESTED
INTERSECTIONS OF ARS 153 2 X , C(X) ARE ACYCLIC 155 2 X , C(X) ARE CRANR
155 2 X , C(X) ARE UNICOHERENT 157 WHITNEY LEVELS IN C(X) ARE CONTINUA
159 2 X , C(X) HAVE TRIVIAL SHAPE 160 ORIGINAL SOURCES 161 EXERCISES 161
20. CONTRACTIBLE HYPERSPACES 164 THE FUNDAMENTAL THEOREM 164 X
CONTRACTIBLE, X HEREDITARILY INDECOMPOSABLE 166 PROPERTY (K) (KELLEY S
PROPERTY) 167 THEOREM ABOUT PROPERTY (K) 168 X PEANO, X HOMOGENEOUS 173
ORIGINAL SOURCES 175 EXERCISES 176 REFERENCES 177 VI. HYPERSPACES AND
THE FIXED POINT PROPERTY 181 21. PRELIMINARIES: BROUWER S THEOREM,
UNIVERSAL MAPS, LOKUCIEWSKI S THEOREM 181 ORIGINAL SOURCES 186 EXERCISES
186 TABLE OF CONTENTS XIII 22. HYPERSPACES WITH THE FIXED POINT PROPERTY
187 PEANO CONTINUA 187 ARC-LIKE CONTINUA 187 CIRCLE-LIKE CONTINUA 190 A
GENERAL THEOREM 192 DENDROIDS 193 HEREDITARILY INDECOMPOSABLE CONTINUA
196 ADDENDUM: DIM[C(X)] 2 196 ORIGINAL SOURCES 197 EXERCISES 197
REFERENCES 199 PART TWO VII. WHITNEY MAPS 205 23. EXISTENCE AND
EXTENSIONS 205 EXERCISES 206 24. OPEN AND MONOTONE WHITNEY MAPS FOR 2 X
207 EXERCISES 215 25. ADMISSIBLE WHITNEY MAPS 216 EXERCISES 225 26. A
METRIC ON HYPERSPACES DEFINED BY WHITNEY MAPS 227 EXERCISES 227
REFERENCES 228 VIII. WHITNEY PROPERTIES AND WHITNEY-REVERSIBLE
PROPERTIES 231 27. DEFINITIONS 231 EXERCISES 233 28. ANR 234 EXERCISES
236 29. APOSYNDESIS 238 EXERCISES 239 30. AR 239 EXERCISES 245 XIV TABLE
OF CONTENTS 31. BEING AN ARC 245 EXERCISES 246 32. ARC-SMOOTHNESS 247
33. ARCWISE CONNECTEDNESS 247 EXERCISES 251 34. BEING ATRIODIC 251
EXERCISES 253 35. C*-SMOOTHNESS, CLASS(W) AND COVERING PROPERTY 253
EXERCISES 256 36. CECH COHOMOLOGY GROUPS, ACYCLICITY 257 37.
CHAINABILITY (ARC-LIKENESS) 257 EXERCISES 259 38. BEING A CIRCLE 259
EXERCISES 259 39. CIRCLE-LIKENESS 259 EXERCISES 260 40. CONE =
HYPERSPACE PROPERTY 261 EXERCISE 262 41. CONTRACTIBILITY 262 EXERCISES
264 42. CONVEX METRIC 265 EXERCISES 265 43. CUT POINTS 265 EXERCISES 267
,44. DECOMPOSABILITY 267 EXERCISES 268 45. DIMENSION 268 EXERCISES 269
46. FIXED POINT PROPERTY 270 EXERCISES 270 47. FUNDAMENTAL GROUP 271
EXERCISES 271 48. HOMOGENEITY 271 EXERCISE 272 49. IRREDUCIBILITY 273
EXERCISES 276 TABLE OF CONTENTS XV 50. KELLEY S PROPERTY 276 EXERCISES
278 51. A-CONNECTEDNESS 279 EXERCISES 280 52. LOCAL CONNECTEDNESS 281
EXERCISES 281 53. N-CONNECTEDNESS 281 EXERCISES 283 54. PLANARITY 283
EXERCISES 284 55. P-LIKENESS 284 EXERCISES 285 56. PSEUDO-ARC 286
EXERCISE 286 57. PSEUDO-SOLENOIDS AND THE PSEUDO-CIRCLE 286 58. R 3
-CONTINUA 286 EXERCISE 287 59. RATIONAL CONTINUA 287 EXERCISES 287 60.
SHAPE OF CONTINUA 287 61. SOLENOIDS 290 62. SPAN 291 63. TREE-LIKENESS
292 64. UNICOHERENCE 292 EXERCISES 293 TABLE SUMMARIZING CHAPTER VIII
294 REFERENCES 299 IX. WHITNEY LEVELS 305 65. FINITE GRAPHS 305
EXERCISES 313 66. SPACES OF THE FORM CE(X,T) ARE ARS 314 EXERCISES . . .
318 67. ABSOLUTELY C*-SMOOTH, CLASS(W) AND COVERING PROPERTY . . 319
EXERCISES 325 XVI TABLE OF CONTENTS 68. HOLES IN WHITNEY LEVELS 326
REFERENCES 329 X. GENERAL PROPERTIES OF HYPERSPACES 333 69.
SEMI-BOUNDARIES 333 EXERCISES 336 70. CELLS IN HYPERSPACES 337 EXERCISES
341 71. NEIGHBORHOODS OF X IN THE HYPERSPACES 342 EXERCISES 344
REFERENCES 345 XI. DIMENSION OF C(X) 347 72. PREVIOUS RESULTS ABOUT
DIMENSION OF HYPERSPACES 347 EXERCISES 348 73. DIMENSION OF C(X) FOR
2-DIMENSIONAL CONTINUA X 349 EXERCISES 357 74. DIMENSION OF C(X) FOR
1-DIMENSIONAL CONTINUA X 358 REFERENCES 359 XII. SPECIAL TYPES OF MAPS
BETWEEN HYPERSPACES 363 75. SELECTIONS 363 EXERCISES 368 76. RETRACTIONS
BETWEEN HYPERSPACES 371 EXERCISES 379 77. INDUCED MAPS 381 EXERCISES 387
REFERENCES 390 XIII. MORE ON CONTRACTIBILITY OF HYPERSPACES 395 78. MORE
ON CONTRACTIBLE HYPERSPACES 395 CONTRACTIBILITY VS. SMOOTHNESS IN
HYPERSPACES 395 R 3 -SETS 399 SPACES OF FINITE SUBSETS 400 ADMISSIBILITY
402 MAPS PRESERVING HYPERSPACE CONTRACTIBILITY 403 TABLE OF CONTENTS
XVII MORE ON KELLEY S PROPERTY 405 EXERCISES 406 REFERENCES 408 XIV.
PRODUCTS, CONES AND HYPERSPACES 413 79. HYPERSPACES WHICH ARE PRODUCTS
413 WRINKLES 414 FOLDS 415 PROOF OF THE MAIN THEOREM 421 EXERCISES 423
80. MORE ON HYPERSPACES AND CONES 424 EXERCISES 431 REFERENCES 434 XV.
QUESTIONS 437 81. UNSOLVED AND PARTIALLY SOLVED QUESTIONS OF [56] 437
82. SOLVED QUESTIONS OF [56] 463 83. MORE QUESTIONS 470 GENERAL SPACES
470 GEOMETRIC MODELS 471 Z-SETS 471 SYMMETRIC PRODUCTS 471 SIZE MAPS 472
THE SPACE OF WHITNEY LEVELS FOR 2 X 473 APOSYNDESIS 473 UNIVERSAL MAPS
473 REFERENCES 474 LITERATURE RELATED TO HYPERSPACES OF CONTINUA SINCE
1978 . . . . 478 SPECIAL SYMBOLS 497 INDEX 499
|
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| spelling | Illanes, Alejandro Verfasser aut Hyperspaces fundamentals and recent advances Alejandro Illanes ; Sam B. Nadler New York [u.a.] Dekker 1999 XVII, 512 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 216 Application Whitney Continu Peano Contractilité hyperespace Géométrie différentielle ram Hyperespace ram Point fixe, Théorème du ram Topologie - Problèmes et exercices ram Hyperspace Hyperraum (DE-588)4161087-8 gnd rswk-swf Hyperraum (DE-588)4161087-8 s DE-604 Nadler, Sam B. Verfasser aut Pure and applied mathematics 216 (DE-604)BV000001885 216 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008364437&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Illanes, Alejandro Nadler, Sam B. Hyperspaces fundamentals and recent advances Pure and applied mathematics Application Whitney Continu Peano Contractilité hyperespace Géométrie différentielle ram Hyperespace ram Point fixe, Théorème du ram Topologie - Problèmes et exercices ram Hyperspace Hyperraum (DE-588)4161087-8 gnd |
| subject_GND | (DE-588)4161087-8 |
| title | Hyperspaces fundamentals and recent advances |
| title_auth | Hyperspaces fundamentals and recent advances |
| title_exact_search | Hyperspaces fundamentals and recent advances |
| title_full | Hyperspaces fundamentals and recent advances Alejandro Illanes ; Sam B. Nadler |
| title_fullStr | Hyperspaces fundamentals and recent advances Alejandro Illanes ; Sam B. Nadler |
| title_full_unstemmed | Hyperspaces fundamentals and recent advances Alejandro Illanes ; Sam B. Nadler |
| title_short | Hyperspaces |
| title_sort | hyperspaces fundamentals and recent advances |
| title_sub | fundamentals and recent advances |
| topic | Application Whitney Continu Peano Contractilité hyperespace Géométrie différentielle ram Hyperespace ram Point fixe, Théorème du ram Topologie - Problèmes et exercices ram Hyperspace Hyperraum (DE-588)4161087-8 gnd |
| topic_facet | Application Whitney Continu Peano Contractilité hyperespace Géométrie différentielle Hyperespace Point fixe, Théorème du Topologie - Problèmes et exercices Hyperspace Hyperraum |
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