Fractals and Universal Spaces in Dimension Theory

• Main Author: Lipscomb, Stephen (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Dynamics.; Ergodic theory.; Functions of complex variables.; Topology.; Analysis.; Functions of a Complex Variable.; Dynamical Systems and Ergodic 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 do...

Table of Contents:

• Construction of =
• Self-Similarity and for Finite
• No-Carry Property of
• Imbedding in Hilbert Space
• Infinite IFS with Attractor
• Dimension Zero
• Decompositions
• The Imbedding Theorem
• Minimal-Exponent Question
• The Imbedding Theorem
• 1992#x2013;2007 -Related Research
• Isotopy Moves into 3-Space
• From 2-Web IFS to 2-Simplex IFS 2-Space and the 1-Sphere
• From 3-Web IFS to 3-Simplex IFS 3-Space and the 2-Sphere.