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 oftopics including point-set topology and mapping theory, fractal geometry, andalgebraic 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. 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 INDICE: 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.
- ISBN: 978-0-387-85493-9
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 242
- Fecha Publicación: 01/02/2009
- Nº Volúmenes: 1
- Idioma: Inglés