Fractals and Universal Spaces in Dimension Theory

Stephen Lipscomb

ISBN 10: 1441927514 / ISBN 13: 9781441927514

Edité par Springer New York, Springer US, 2010

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 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.

N° de réf. du vendeur 9781441927514

Détails bibliographiques

• Titre: Fractals and Universal Spaces in Dimension Theory
• Éditeur: Springer New York, Springer US
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 1441927514
• ISBN à 13 chiffres: 9781441927514
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 15 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 15 millimètres de profondeur
• Poids: 411 grammes

A propos de ce titre

Synopsis

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.

Présentation de l'éditeur

For metric spaces the quest for universal spaces in dimension theory spanned a century of research, which breaks into two periods: the classical (separable metric) and the modern (not necessarily separable metric). This book details the modern theory.