Kelley doctoral dissertation was published, the hyperspace theory became an important way of obtaining information on the structure of a topological space X by studying properties of the hyper-space 2, and its hyperspaces. Dekker New York Wikipedia Citation Please see Wikipedia's template documentation for further citation fields that may be required. The reader is referred to for an outline of history and for a further information in this area. 1978, Hyperspaces of sets : a text with research questions / Sam B. In particular, it is shown in that paper that if X is metric and compact, then the Vietoris topology coincides with the one introduced by the Hausdorfi metric. Search 204,770,711 papers from all fields of science. Skip to search form Skip to main content Skip to account menu. Semantic Scholar extracted view of 'Hyperspaces of compact convex sets' by S. Topologies on these and other families of subsets of a topological space X were studied by E. A text with research questions, Monographs and Textbooks in Pure and Applied Mathematics 49, Marcel Dekker, Inc., New York-Basel, 1978. Semantic Scholar extracted view of 'Hyperspaces of compact convex sets' by S. In case when X is a metric space, the family of all bounded nonempty closed subsets of X can be metrized by the Hausdorfi metric (distance), in-troduced by Hausdorfi in 1914.
#KURATOWSKI NADLER HYPERSPACES UPGRADE#
that compactness (similarly connectedness) of 2, is equivalent to that of X. System Upgrade on Mon, Jun 21st, 2021 at 1am (EDT) During this period, the E-commerce and registration of new users may not be available for up to 6 hours. Vietoris proved the most basic facts of the structure of 2, as e. Gi-ven a topological space X, the hyperspace 2, of all nonempty closed subsets of X is equipped with the Vietoris topology, also called the exponential topo-logy, see or the finite topology, see, introduced in 1922 by Vietoris. Kato, On scrambled sets and a theorem of Kuratowski on independent sets. Hyperspace theory has its beginnings in the early years of XX century with the work of Felix Hausdorfi (1868-1942) and Leopold Vietoris (1891-2002). Nadler, Hyperspaces, Fundamentals and recent advances.