Fractals and Universal Spaces in Dimension Theory

ebook Springer Monographs in Mathematics

By Stephen Lipscomb

cover image of Fractals and Universal Spaces in Dimension Theory

Sign up to save your library

With an OverDrive account, you can save your favorite libraries for at-a-glance information about availability. Find out more about OverDrive accounts.

   Not today

Find this title in Libby, the library reading app by OverDrive.

Download Libby on the App Store Download Libby on Google Play

Search for a digital library with this title

Title found at these libraries:

Library Name Distance
Loading...

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.

Fractals and Universal Spaces in Dimension Theory