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110406s2009 xxu| s |||| 0|eng d |
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|a 9780387854946
|9 978-0-387-85494-6
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|a 10.1007/978-0-387-85494-6
|2 doi
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| 100 |
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|a Lipscomb, Stephen.
|e author.
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|a Fractals and Universal Spaces in Dimension Theory
|c by Stephen Lipscomb.
|h [electronic resource] /
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|a New York, NY :
|b Springer New York,
|c 2009.
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| 300 |
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|a XVIII, 242p. 91 illus., 15 illus. in color.
|b online resource.
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| 336 |
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|a text
|b txt
|2 rdacontent
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| 337 |
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|a computer
|b c
|2 rdamedia
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| 338 |
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|a online resource
|b cr
|2 rdacarrier
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| 347 |
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|a text file
|b PDF
|2 rda
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| 490 |
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|a Springer Monographs in Mathematics,
|x 1439-7382
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| 505 |
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|a Preface -- Introduction -- Construction of JA=j alpha -- Self-Similarity and Jn+1 for Finite n -- No-Carry Property of wA -- Imbedding Ja in Hilbert Space -- Infinite IFS with Attractor wA -- Infinite IFS with Attractor wA -- Dimension Zero -- Decompositions -- The Jn+1 Imbedding Theorem -- Minimal-Exponent Question -- The JA Imbedding Theorem -- 1992-2007 Ja Related Research -- Isotopy Moves J5 Into 3-Space -- From 2-Web IFS to 2 Simplex IFS 2-Space and the 1-Sphere -- From 3-Web IFS to 3-Simplex 3-Space and the 2-Sphere -- Background Basics -- The Standard Simplex -- Measures and Fractal Dimension -- Bibliography -- Index.
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| 520 |
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|a 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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| 650 |
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|a Mathematics.
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| 650 |
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|a Global analysis (Mathematics).
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| 650 |
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|a Differentiable dynamical systems.
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| 650 |
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|a Functions of complex variables.
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| 650 |
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|a Topology.
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| 650 |
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|a Mathematics.
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| 650 |
2 |
4 |
|a Topology.
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| 650 |
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4 |
|a Analysis.
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| 650 |
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|a Functions of a Complex Variable.
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| 650 |
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|a Dynamical Systems and Ergodic Theory.
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 773 |
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|t Springer eBooks
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| 776 |
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|i Printed edition:
|z 9780387854939
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| 830 |
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|a Springer Monographs in Mathematics,
|x 1439-7382
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| 856 |
4 |
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|u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-85494-6
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| 912 |
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|a ZDB-2-SMA
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| 950 |
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|a Mathematics and Statistics (Springer-11649)
|