|Statement||Sam B. Nadler, Jr.|
|Series||Monographs and textbooks in pure and applied mathematics ; v. 49|
|LC Classifications||QA691 .N25|
|The Physical Object|
|Pagination||xvi, 707 p. ;|
|Number of Pages||707|
|LC Control Number||78009013|
Se- VI HYPERSPACES OF SETS vii lections are discussed from the viewpoint of selections from sub- spaces of 2 and С (X) rather than from the viewpoint of selec- selections for set-valued mappings. This is in keeping with the empha- emphasis of the book. Hyperspaces of sets: a text with research questions. [Sam B Nadler] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Book, Internet Resource: All Authors / Contributors: Sam B Nadler. Find more information about: ISBN: OCLC Number: Hyperspaces of Sets: A Text with Research Questions (Monographs and Textbooks in Pure and Applied Mathematics) by Sam B. Nadler. Write a review. How does Amazon calculate star ratings?5/5. 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. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before.
Australian/Harvard Citation. Nadler, Sam B. , Hyperspaces of sets: a text with research questions / Sam B. Nadler, Jr M. Dekker New York. Wikipedia Citation. Please see Wikipedia's template documentation for further citation fields that may be required. To define the various topologies on the collection of closed subsets of a space X, certain collection of sets are considered. When these collections are topologized, they are called hyperspaces of X. Hyperspaces of non-cut sets of locally connected continua As we quoted in Remark , for any locally connected continuum X it holds that N W C (X) = N C (X). Thus, in this case, by Theorem , we have that all of the hyperspaces of non-cut sets coincide. Given a compact and connected metric space (continuum) X, we study topological and dynamical properties of the hyperspace of normal fuzzy sets F 1 (X) equipped with the Hausdorff, endograph or sendograph metric. Among the many results we show that it is contractible, path connected, locally contractible, locally path connected, locally simply connected and locally connected.
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. 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. In particular, they study the related classes of inclusion hyperspaces and growth hyperspaces. A closed subset E of 2 X is an inclusion hyperspace provided that it is closed under upward inclusion, i.e., A ∈ I if for some B ∈ I, B ⊆ A; E is a growth hyperspace if A ∈ E provided that for some B ∈ E, B ⊆ A and each component of A meets B. HYPERSPACES OF SETS. A TEXT WITH RESEARCH QUESTIONS. SAM B. NADLER, JR. SUB Gottingen A SOCIEDAD MATEMATICA MEXICANA CONTENTS ABOUT THE BOOK ix USING THE BOOK IN A BEGINNING TOPOLOGY COURSE. xiii A VERY BRIEF HISTORY OF HYPERSPACE THEORY xvii ACKNOWLEDGMENTS xix CHAPTER 0 SOME . We study the interaction of some dynamical properties of a nonautonomous discrete dynamical system (X, f ∞) and its induced nonautonomous discrete dynamical system (K (X), f ∞ ¯), where K (X) is the hyperspace of non-empty compact sets in X, endowed with the Vietoris consider properties like transitivity, weakly mixing, points with dense orbit, density of periodic points.