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Fractals and Universal Spaces in Dimension Theory
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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 of this title 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 that contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings; and, various chapters that contain 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.
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