![]() ![]() ![]() In Chapter 3, a one-parameter family of gauge functions is constructed which computes the dimensions of the hyperspaces of graph-self-similar sets that satisfy the Strong Separation Condition, after which the approximations of Chapter 2 are applied to extend the result to graph-self-similar sets which satisfy the Open Set Condition. known topologies on hyperspaces, we investigate the characterizations of statistical convergence of sequences of sets in the realm of these structures. In Chapter 2 it is shown that the dimensions of the underlying fractals may be approximated by the dimensions of sets invariant under particularly constructed subiterated function systems that satisfy the Strong Separation Condition. ![]() This dissertation further generalizes these results to include graph-self-similar and self-conformal fractals satisfying the Open Set Condition in Rd. In this paper, we mainly discuss the hyperspace when is an infinite countable discrete space. Hyperspaces have been extensively studied by topologists since the 1970's, but the measure theoretical study of hyperspaces has lagged, Boardman and Goodey concurrently provided a characterization of a one-parameter family of Hausdorff gauge functions that determine the dimension of H(), and this result was extended by McClure to H(X) where X is a self-similar fractal satisfying the Open Set Condition. A note on hyperspaces by closed sets with Vietoris topology Chuan Liu, Fucai Lin For a topological space, let be the set of all non-empty closed subset of, and denote the set with the Vietoris topology by. H(K) is itself a metric space under the Hausdorff metric dH. These ideas have considerable scope for further development, and a list of problems and lines of research is included.Given a metric space (K, d), the hyperspace of K is defined by H(K) =. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are visually fractal, i.e. The last and most original part of the book introduces the notion of a view as part of a framework for studying the structure of sets within a given space. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. In this paper it is investigated as to when a nonempty invariant closed subset A of a S1 -space X containing the set of stationary points (S) can be the. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. The hyperspaces and are subjects of study for many researchers. In turn, the hyperspace of all nonempty, closed, and connected sets of X containing a point p, which is denoted by, is a subspace of. ![]() Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. Set a custom desktop image for each of your Spaces and watch as the pictures fade into each other when switching Spaces. The hyperspace of all nonempty, closed and connected subsets of X is denoted by and considered as a subspace of. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |