Overview
- Author includes more than 60 bw illustrations and 15 in color
- Each chapter contains comments that provide historical context
- This is the first time most of this material has appeared in book form
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Historically, 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).
The classical theory is now well documented in several books. This monograph is the first book to unify the modern theory from 1960-2007. Like the classical theory, the modern theory fundamentally involves the unit interval.
Unique features include:
* The use of graphics to illustrate the fractal view of these spaces;
* Lucid coverage of a range of topics including point-set topology and mapping theory, fractal geometry, and algebraic topology;
* A final chapter contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings;
* Each chapter contains a comment section that provides historical context with references that serve as a bridge to the literature.
This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. Being the first monograph to focus on the connection between generalized fractals and universal spaces in dimension theory, it will be a natural text for graduate seminars or self-study - the interested reader will find many relevant open problems which will create further research into these topics.
Reviews
From the reviews:
“The book is a research monograph reporting on an interesting area of research arising from the confluence of two streams: topology and self-similar fractals. It is written at a level that could be understood by graduate students and advanced undergraduates. It could be used for a seminar or introductory course for either topology or self-similar sets. … The historical notes are informative and interesting. There is an extensive bibliography at the end of the book documenting the results and historical comments.” (J. E. Keesling, Mathematical Reviews, Issue 2011 b)
“The book under review is devoted to dimension theory in general. … The book is completed by a useful appendix consisting of three parts, devoted to basics in topology, standard simplices in Hilbert spaces, and fractal geometry. So, it is accessible for all mathematicians, but should be of special interest for those working in topology or fractal geometry. The book contains a remarkable number of interesting historical remarks and colorful pictures.” (Uta Freiberg, Zentralblatt MATH, Vol. 1210, 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Fractals and Universal Spaces in Dimension Theory
Authors: Stephen Lipscomb
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-0-387-85494-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2009
Hardcover ISBN: 978-0-387-85493-9Published: 03 December 2008
Softcover ISBN: 978-1-4419-2751-4Published: 29 November 2010
eBook ISBN: 978-0-387-85494-6Published: 28 October 2008
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XVIII, 242
Number of Illustrations: 76 b/w illustrations, 15 illustrations in colour
Topics: Topology, Analysis, Functions of a Complex Variable, Dynamical Systems and Ergodic Theory