When does the Fell topology on a hyperspace of closed sets coincide with the meet of the upper Kuratowski and the lower Vietoris topologies?

DOI10.1016/0166-8641(95)00098-4zbMath0848.54007OpenAlexW2086631254MaRDI QIDQ1917060

Tsugunori Nogura, Dmitrij B. Shakhmatov

Publication date: 28 October 1996

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(95)00098-4

zbMATH Keywords

consonant spacesFell topologyconsonanceupper Kuratowski topologyupper Kuratowski-Painlevé convergence

Mathematics Subject Classification ID

Hyperspaces in general topology (54B20) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Connections of general topology with other structures, applications (54H99) (k)-spaces (54D50)

Related Items (37)

Some open problems on well-filtered spaces and sober spaces ⋮ Domain-complete and LCS-complete spaces ⋮ Core-compactness, consonance and the Smyth powerspaces ⋮ Selection principles of the Fell topology and the Vietoris topology ⋮ Unnamed Item ⋮ Borel measures in consonant spaces ⋮ A framework of induced hyperspace dynamical systems equipped with the hit-or-miss topology ⋮ Characterizing ergodicity of induced hyperspace dynamical systems ⋮ Complements of consonant spaces in complete spaces ⋮ Consonance and Cantor set-selectors ⋮ \({\mathbf H}\)-trivial spaces ⋮ Erratum to ``Coincidence of function space topologies [Topology Appl. 157 (2) (2010) 336-351] ⋮ Coincidence of the Isbell and fine Isbell topologies ⋮ First-countability, sequentiality and tightness of the upper Kuratowski convergence ⋮ F-sensitivity and (F_1, F_2)-sensitivity between dynamical systems and their induced hyperspace dynamical systems ⋮ Fell topology on the hyperspace of a non-Hausdorff space ⋮ (Ultra-) completeness numbers and (pseudo-) paving numbers ⋮ Range universal spaces ⋮ On products of consonant spaces ⋮ Completeness, sections and selections ⋮ Variations of consonance and the rational numbers ⋮ Characterizing mixing, weak mixing and transitivity of induced hyperspace dynamical systems ⋮ Open quotients of trivial vector bundles ⋮ Dynamical systems over the space of upper semicontinuous fuzzy sets ⋮ On metrization of the hit-or-miss topology using Alexandroff compactification ⋮ An infraconsonant nonconsonant completely regular space ⋮ On hereditary Baireness of the Vietoris topology ⋮ On the upper semicontinuity of Choquet capacities ⋮ Base-complexity classifications of qcb0-spaces1 ⋮ Sensitive dependence on initial conditions between dynamical systems and their induced hyperspace dynamical systems ⋮ On the instability of a topological game related to consonance ⋮ Consonant spaces and topological games ⋮ Two topologies on the lattice of Scott closed subsets ⋮ Coincidence of function space topologies ⋮ A note on consonance of \(G_\delta\) subsets ⋮ On the dissonance of some metrizable spaces ⋮ Coincidence of the upper Kuratowski topology with the co-compact topology on compact sets, and the Prohorov property

Cites Work

• The structure of algebras of operator fields
• Convergence and existence of random set distributions
• On Vervaat's sup vague topology
• Random capacities and their distributions
• Set theory. An introduction to independence proofs
• Concerning topological convergence of sets
• On open mappings, II
• A Hausdorff Topology for the Closed Subsets of a Locally Compact Non-Hausdorff Space
• On topologies generating the Effros Borel structure and on the Effros measurability of the boundary operation
• When do the Upper Kuratowski Topology (Homeomorphically, Scott Topology) and the Co-compact Topology Coincide?
• Convergence of Closed Subsets in a Topological Space
• Internal cohen extensions
• Verschiedene Topologisierungen im Raum der abgeschlossenen Mengen
• Note on Convergence in Topology
• Wild 0-dimensional sets and the fundamental group
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: When does the Fell topology on a hyperspace of closed sets coincide with the meet of the upper Kuratowski and the lower Vietoris topologies?