Fractals and Universal Spaces in Dimension Theory

• Main Author: Lipscomb, Stephen. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Global analysis (Mathematics).; Differentiable dynamical systems.; Functions of complex variables.; Topology.; Analysis.; Functions of a Complex Variable.; Dynamical Systems and Ergodic Theory.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-85494-6

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 do...

Table of Contents:

• 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.