Measure, topology, and fractal geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1995
|
| Ausgabe: | Corr. 3. print. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 230 S. Ill. |
| ISBN: | 0387972722 3540972722 |
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Datensatz im Suchindex
| _version_ | 1804135885216677888 |
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| adam_text | GERALD A. EDGAR MEASURE, TOPOLOGY, AND FRACTAL GEOMETRY WITH 96
ILLUSTRATIONS AND 16 COLOR PLATES ; *** SPRINGER F CONTENTS PREFACE V
CHAPTER 1. FRACTAL EXAMPLES 1.1. THE TRIADIC CANTOR DUST 1 1.2. THE
SIERPINSKI GASKET 7 1.3. A SPACE OF STRINGS 11 1.4. TURTLE GRAPHICS 14
1.5. SETS DEFINED RECURSIVELY 18 1.6. NUMBER SYSTEMS 28 *1.7. REMARKS 32
CHAPTER 2. METRIE TOPOLOGY 2.1. METRIE SPACES 37 2.2. SEPARABLE AND
COMPACT SPACES 52 2.3. UNIFORM CONVERGENCE 60 2.4. THE HAUSDORFF METRIE
65 2.5. METRICS FOR STRINGS 69 *2.6. REMARKS 75 CHAPTER 3. TOPOLOGICAL
DIMENSION 3.1. SMALL INDUCTIVE DIMENSION 79 3.2. LAERGE INDUCTIVE
DIMENSION 84 *3.3. TWO-DIMENSIONAL EUCLIDEAN SPACE 90 *3.4. OTHER
TOPOLOGICAL DIMENSIONS 95 *3.5. REMARKS 103 CHAPTER 4. SELF-SIMILARITY
4.1. RATIO LISTS 105 4.2. STRING MODELS 110 4.3. GRAPH SELF-SIMILARITY
113 *4.4. REMARKS 120 CHAPTER 5. MEASURE THEORY 5.1. LEBESGUE MEASURE
123 5.2. METHOD I 132 5.3. TWO-DIMENSIONAL LEBESGUE MEASURE 139 5.4.
METHOD II 141 5.5. MEASURES FOR STRINGS 142 *5.6. REMARKS 144 CHAPTER 6.
HAUSDORFF DIMENSION 6.1. HAUSDORFF MEASURE 147 6.2. EXAMPLES 151 6.3.
SELF-SIMILARITY 156 6.4. GRAPH SELF-SIMILARITY 167 *6.5. OTHER FRACTAL
DIMENSIONS 179 *6.6. REMARKS 186 CHAPTER 7. ADDITIONAL TOPICS *7.1. A
THREE-DIMENSIONAL DRAGON 195 *7.2. OVERLAP 198 *7.3. SELF-AFFINE SETS
200 *7.4. OTHER EXAMPLES 205 *7.5. REMARKS 212 APPENDIX TERMS 217
NOTATION 220 EXAMPLES 221 READING 221 REFERENCES 223 INDEX 225
|
| adam_txt |
GERALD A. EDGAR MEASURE, TOPOLOGY, AND FRACTAL GEOMETRY WITH 96
ILLUSTRATIONS AND 16 COLOR PLATES ; *** SPRINGER F CONTENTS PREFACE V
CHAPTER 1. FRACTAL EXAMPLES 1.1. THE TRIADIC CANTOR DUST 1 1.2. THE
SIERPINSKI GASKET 7 1.3. A SPACE OF STRINGS 11 1.4. TURTLE GRAPHICS 14
1.5. SETS DEFINED RECURSIVELY 18 1.6. NUMBER SYSTEMS 28 *1.7. REMARKS 32
CHAPTER 2. METRIE TOPOLOGY 2.1. METRIE SPACES 37 2.2. SEPARABLE AND
COMPACT SPACES 52 2.3. UNIFORM CONVERGENCE 60 2.4. THE HAUSDORFF METRIE
65 2.5. METRICS FOR STRINGS 69 *2.6. REMARKS 75 CHAPTER 3. TOPOLOGICAL
DIMENSION 3.1. SMALL INDUCTIVE DIMENSION 79 3.2. LAERGE INDUCTIVE
DIMENSION 84 *3.3. TWO-DIMENSIONAL EUCLIDEAN SPACE 90 *3.4. OTHER
TOPOLOGICAL DIMENSIONS 95 *3.5. REMARKS 103 CHAPTER 4. SELF-SIMILARITY
4.1. RATIO LISTS 105 4.2. STRING MODELS 110 4.3. GRAPH SELF-SIMILARITY
113 *4.4. REMARKS 120 CHAPTER 5. MEASURE THEORY 5.1. LEBESGUE MEASURE
123 5.2. METHOD I 132 5.3. TWO-DIMENSIONAL LEBESGUE MEASURE 139 5.4.
METHOD II 141 5.5. MEASURES FOR STRINGS 142 *5.6. REMARKS 144 CHAPTER 6.
HAUSDORFF DIMENSION 6.1. HAUSDORFF MEASURE 147 6.2. EXAMPLES 151 6.3.
SELF-SIMILARITY 156 6.4. GRAPH SELF-SIMILARITY 167 *6.5. OTHER FRACTAL
DIMENSIONS 179 *6.6. REMARKS 186 CHAPTER 7. ADDITIONAL TOPICS *7.1. A
THREE-DIMENSIONAL DRAGON 195 *7.2. OVERLAP 198 *7.3. SELF-AFFINE SETS
200 *7.4. OTHER EXAMPLES 205 *7.5. REMARKS 212 APPENDIX TERMS 217
NOTATION 220 EXAMPLES 221 READING 221 REFERENCES 223 INDEX 225 |
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| dewey-full | 514.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Corr. 3. print. |
| format | Book |
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| id | DE-604.BV021928932 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:06:10Z |
| indexdate | 2024-07-09T20:47:37Z |
| institution | BVB |
| isbn | 0387972722 3540972722 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015144089 |
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| physical | IX, 230 S. Ill. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Edgar, Gerald A. 1949- Verfasser (DE-588)112698808 aut Measure, topology, and fractal geometry Gerald A. Edgar Corr. 3. print. New York [u.a.] Springer 1995 IX, 230 S. Ill. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Fractals Measure theory Topology Fraktal (DE-588)4123220-3 gnd rswk-swf Metrik Mathematik (DE-588)4193458-1 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Fraktalgeometrie (DE-588)4473576-5 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Metrik Mathematik (DE-588)4193458-1 s Topologie (DE-588)4060425-1 s Geometrie (DE-588)4020236-7 s Fraktal (DE-588)4123220-3 s 2\p DE-604 Maßtheorie (DE-588)4074626-4 s 3\p DE-604 Fraktalgeometrie (DE-588)4473576-5 s 4\p DE-604 5\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015144089&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Edgar, Gerald A. 1949- Measure, topology, and fractal geometry Fractals Measure theory Topology Fraktal (DE-588)4123220-3 gnd Metrik Mathematik (DE-588)4193458-1 gnd Maßtheorie (DE-588)4074626-4 gnd Fraktalgeometrie (DE-588)4473576-5 gnd Geometrie (DE-588)4020236-7 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4123220-3 (DE-588)4193458-1 (DE-588)4074626-4 (DE-588)4473576-5 (DE-588)4020236-7 (DE-588)4060425-1 (DE-588)4123623-3 |
| title | Measure, topology, and fractal geometry |
| title_auth | Measure, topology, and fractal geometry |
| title_exact_search | Measure, topology, and fractal geometry |
| title_exact_search_txtP | Measure, topology, and fractal geometry |
| title_full | Measure, topology, and fractal geometry Gerald A. Edgar |
| title_fullStr | Measure, topology, and fractal geometry Gerald A. Edgar |
| title_full_unstemmed | Measure, topology, and fractal geometry Gerald A. Edgar |
| title_short | Measure, topology, and fractal geometry |
| title_sort | measure topology and fractal geometry |
| topic | Fractals Measure theory Topology Fraktal (DE-588)4123220-3 gnd Metrik Mathematik (DE-588)4193458-1 gnd Maßtheorie (DE-588)4074626-4 gnd Fraktalgeometrie (DE-588)4473576-5 gnd Geometrie (DE-588)4020236-7 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Fractals Measure theory Topology Fraktal Metrik Mathematik Maßtheorie Fraktalgeometrie Geometrie Topologie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015144089&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT edgargeralda measuretopologyandfractalgeometry |