Fractals and Universal Spaces in Dimension Theory

• 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.

From the reviews: "The book is a research monograph reporting on an interesting area of research arising from the confluence of two streams: topology and self-similar fractals. It is written at a level that could be understood by graduate students and advanced undergraduates. It could be used for a seminar or introductory course for either topology or self-similar sets. ... The historical notes are informative and interesting. There is an extensive bibliography at the end of the book documenting the results and historical comments." (J. E. Keesling, Mathematical Reviews, Issue 2011 b) "The book under review is devoted to dimension theory in general. ... The book is completed by a useful appendix consisting of three parts, devoted to basics in topology, standard simplices in Hilbert spaces, and fractal geometry. So, it is accessible for all mathematicians, but should be of special interest for those working in topology or fractal geometry. The book contains a remarkable number of interesting historical remarks and colorful pictures." (Uta Freiberg, Zentralblatt MATH, Vol. 1210, 2011)