We discuss the following subjects: (1) Introduction to general topology, hyperspaces, metric and pseudometric spaces, graph theory. Sünderhauf, Quasi-uniform completeness in terms of Cauchy nets, Acta Math. The course was given at Peking University, Fall 2019.
Sánchez-Granero, Compactifications of quasi-uniform hyperspaces, Topology Appl., 127 (2003), 409–423. Romaguera, Wijsman and hit-and-miss topologies of quasimetric spaces, Set-Valued Analysis, 11 (2003), 323–344. Romaguera, The relationship between the Vietoris topology and the Hausdorff quasi-uniformity, Topology Appl., 124 (2002), 451–464. CrossRef View Record in Scopus Google Scholar. On the equivalence of normality and compactness in hyperspaces. Schellekens, On the Yoneda completion of a quasi-metric space, Theoretical Computer Science, 278 (2002), 159–194. Some of the results of the study of basic properties such as compactness, connectedness, and separation axioms are that X is regular if and only if.
#Compactness of hyperspaces download
Romaguera, Quasi-metric spaces, quasi-metric hyperspaces and uniform local compactness, Rend. Download Citation Local Compactness of Hyperspaces The points of local compactness of 2(X), the set of dosed nonempty subsets of a space X, with the Vietoris 6 topology, turn out to be the. Romaguera, Left K-completeness of the Hausdorff quasiuniformity, Rostocker Math. Künzi, Quasi-metrizable spaces satisfying certain completeness conditions, Acta Math. Künzi, Nonsymmetric topology, in: Proceedings of Colloquium on Topology (Szekszárd, Hungary, 1993), Colloquium Mathematical Society János Bolyai Mathematic Studies, 4 (1995), 303–338. Let X be a regular Ti topological space and 2X the space of all closed nonempty subsets of X with. Hunsaker, Symmetric conditions in terms of open sets, Topology Appl., 45 (1992), 39–47. Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. (eds) Set-Valued Mappings, Selections and Topological Properties of 2x. Abstract: In this paper, some topological properties, especially those that associated with compactness properties as in 8 were studied on hyperspaces and of X and compared with the original space Keywords: - closed set, Z closed set, Lindelöf space, Extremely disconnected space, Paracompact space, hereditary disconnected. Some Results on the Countable Compactness and Pseudocompactness of Hyperspaces - Volume 27 Issue 6. Lindgren, Quasi-uniform Spaces, Marcel Dekker (New York, 1982). Compactness related properties in hyperspaces. Heckmann, A computational model for metric spaces, Theoretical Computer Science, 193 (1995), 53–73. Edalat, Domains for computation in mathematics, physics and exact real arithmetic, Bulletin of Symbolic Logic, 3 (1997), 401–452.Ī. Edalat, Dynamical systems, measures and fractals via domain theory, Information and Computation, 120 (1995), 32–48.Ī. Bella, Some observations on indestructible compact spaces, Topology Appl.
Rodríguez-López, On hyperspace topologies via distance functionals in quasi-metric spaces, Acta Math. Sakai, Tight points of Pixley- Roy hyperspaces, Topology Appl. Romaguera, Quasi-uniform hyperspaces of compact subsets, Topology Appl., 87 (1998), 117–126. Moreover, if d is a T 1 quasi-metric, then the hyperspace is algebraic, and the set of all finite subsets forms a base for it. We show that K 0(X), equipped with the Hausdorff quasi-pseudometric H d forms a (sequentially) Yoneda-complete space. Rutten, Generalized metric spaces: Completion, topology and powerdomains via the Yoneda embedding, Theoretical Computer Science, 193 (1998), 1–51. We study the hyperspace K 0(X) of non-empty compact subsets of a Smyth-complete quasi-metric space (X, d). Beer, Topologies on Closed and Closed Convex Sets, Kluwer Academic Publishers (Dordrecht, 1993). L K be a compact convex subset of a metriz- able locally convex real topological vector space L, dimK 2. Alimov, On the structure of the complements of Chebyshev sets, Functional Analysis and Its Applications, 35 (2001), 176–182. Reed (ed.), Set-Theoretic Topology, Acad. van Douwen, "The Pixley–Roy topology on spaces of subsets" G.M. McAllister, "Hyperspaces and multifunctions, the first half century" Nieuw Arch. Mostly emphasized are compactness properties for hit-and-miss topologies from. Hung, Characterization of bases of countable order and factorization of monotone developability, Top. Vietoris, "Bereiche zweiter Ordnung" Monatsh. Hyperspaces are studied for topological spaces as well as for multifilter spaces. Knzi, Properties related to compactness in hyperspaces, Top. Let X be a regular Ti topological space and 2X the space of all closed nonempty subsets of X with the finite topology 8, Definition 1.7. It is often used in the construction of counterexamples, see. COMPACTNESS IN HYPERSPACES JAMES KEESLING Introduction. A space whose points are the elements of some family $\mathfrak_\omega(X)$ is called the Pixley–Roy hyperspace of $X$.
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