The Collins-Roscoe property and its applications in the theory of function spaces

DOI10.1016/j.topol.2010.08.022zbMath1245.54022OpenAlexW1965792223MaRDI QIDQ408557

Vladimir V. Tkachuk

Publication date: 10 April 2012

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

Full work available at URL: https://doi.org/10.1016/j.topol.2010.08.022

zbMATH Keywords

\(\sigma\)-productLindelöf \(\Sigma\)-space(hereditarily) metalindelöf space(iterated) function spaces(strongly) monotonically monolithic space\(D\)-spaces\(T_0\)-separating familycaliberCollins-Roscoe propertyweakly \(\sigma\)-point-finite family

Mathematics Subject Classification ID

Continuous maps (54C05) Function spaces in general topology (54C35) Compactness (54D30) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Product spaces in general topology (54B10) Stratifiable spaces, cosmic spaces, etc. (54E20)

Related Items (14)

A study on \(D\)-spaces and the metrizability of compact spaces with property (\(\sigma \)-A) ⋮ More about Collins-Roscoe property in function spaces ⋮ A study on symmetric products of generalized metric spaces ⋮ A note on \(D\)-property, monotone monolithicity and \(\sigma\)-product ⋮ Hereditarily monotonically Sokolov spaces have countable network weight ⋮ Projectively first-countable semitopological groups with certain \(D\)-properties ⋮ Countably compact spaces with \(n\)-in-countable weak bases are metrizable ⋮ Every \(\Sigma_{s}\)-product of \(K\)-analytic spaces has the Lindelöf {\(\Sigma\)}-property ⋮ Existence of nice weak bases implies the \(D\)-property ⋮ Monotonically monolithic spaces, Corson compacts, and \(D\)-spaces ⋮ Notes on the Collins-Roscoe property and \(D\)-spaces ⋮ Unnamed Item ⋮ Some sufficiency conditions for \(D\)-spaces, dually discrete and its applications ⋮ \(D\)-property, monotone monolithicity and function spaces

Cites Work

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• Monotonically monolithic spaces, Corson compacts, and \(D\)-spaces
• On Lindelöf \(\Sigma\)-spaces of continuous functions in the pointwise topology
• Monolithic spaces and \(D\)-spaces revisited
• A note on the point-countable base question
• Behavior of the Lindelöf \(\Sigma\)-property in iterated function spaces
• A broader context for monotonically monolithic spaces
• Criteria for Metrisability
• A Lattice of Conditions on Topological Spaces
• Topological Spaces with Point-Networks
• A lattice of conditions on topological spaces II
• Weak Covering Properties of Weak Topologies

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