Coincidence of function space topologies

DOI10.1016/J.TOPOL.2009.09.002zbMath1187.54016OpenAlexW1988680638MaRDI QIDQ1044865

Francis Jordan

Publication date: 15 December 2009

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

Full work available at URL: https://doi.org/10.1016/j.topol.2009.09.002

zbMATH Keywords

lower semicontinuouscompact-open topologyfunction spaceconcordantharmonicupper semicontinuousIsbell topologynatural topologyconsonant

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Consistency and independence results in general topology (54A35)

Related Items (11)

When the finest splitting topology is a group topology or Fréchet ⋮ Dual uniformities in function spaces over uniform continuity ⋮ Erratum to ``Coincidence of function space topologies [Topology Appl. 157 (2) (2010) 336-351] ⋮ Coincidence of the Isbell and fine Isbell topologies ⋮ Range universal spaces ⋮ Variations of consonance and the rational numbers ⋮ An infraconsonant nonconsonant completely regular space ⋮ Group topologies coarser than the Isbell topology ⋮ A study of uniformities on the space of uniformly continuous mappings ⋮ Consonant spaces and topological games ⋮ A study of topological structures on equi-continuous mappings

Cites Work

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• On the compact open and finest splitting topologies
• On the greatest splitting topology
• A note on consonance of \(G_\delta\) subsets
• On the dissonance of some metrizable spaces
• On the coincidence of the upper Kuratowski topology with the cocompact topology
• \({\mathbf H}\)-trivial spaces
• First-countability, sequentiality and tightness of the upper Kuratowski convergence
• Coincidence of the upper Kuratowski topology with the co-compact topology on compact sets, and the Prohorov property
• When does the Fell topology on a hyperspace of closed sets coincide with the meet of the upper Kuratowski and the lower Vietoris topologies?
• Topologies for function spaces
• The Spectral Theory of Distributive Continuous Lattices
• When do the Upper Kuratowski Topology (Homeomorphically, Scott Topology) and the Co-compact Topology Coincide?

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