Fractals and universal spaces in dimension theory
For metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods the classical (separable metric) and the modern (not necessarily separable metric). While the classical theory is now well docu...
Guardat en:
| Autor principal: | |
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| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2009. |
| Col·lecció: | Springer Monographs in Mathematics
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| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'après consultation du 20 octobre 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Fractals and universal spaces in dimension theory, Stephen Lipscomb, [New York], Springer, 2009, 1 vol. (xvii-241 p.-[8] p. de pl.), Springer monographs in mathematics, 978-0-387-85493-9 • Fractals and Universal Spaces in Dimension Theory, Texte imprimé, 9781441927514 • Fractals and Universal Spaces in Dimension Theory, Texte imprimé, 9780387855370 • Fractals and universal spaces in dimension theory, Stephen Lipscomb, [New York], Springer, 2009, 1 vol. (xvii-241 p.-[8] p. de pl.), Springer monographs in mathematics, 978-0-387-85493-9 |
| Sumari: | For metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods the classical (separable metric) and the modern (not necessarily separable metric). While the classical theory is now well documented in several books, this is the first book to unify the modern theory (1960 2007). Like the classical theory, the modern theory fundamentally involves the unit interval. By the 1970s, the author of this monograph generalized Cantor s 1883 construction (identify adjacent-endpoints in Cantor s set) of the unit interval, obtaining for any given weight a one-dimensional metric space that contains rationals and irrationals as counterparts to those in the unit interval. Following the development of fractal geometry during the 1980s, these new spaces turned out to be the first examples of attractors of infinite iterated function systems generalized fractals. The use of graphics to illustrate the fractal view of these spaces is a unique feature of this monograph. In addition, this book provides historical context for related research that includes imbedding theorems, graph theory, and closed imbeddings. This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. It can also serve as a text for graduate seminars or self-study the interested reader will find many relevant open problems that will motivate further research into these topics |
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| Descripció de l’ítem: | Description d'après consultation du 20 octobre 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografia: | Bibliogr. Index |
| ISBN: | 9780387854946 |
| ISSN: | 2196-9922 |
| Accés: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |