A Lattice of Conditions on Topological Spaces

DOI10.2307/2045241zbMath0562.54043OpenAlexW4249996080MaRDI QIDQ3675179

A. W. Roscoe, G. M. Reed, Mary Ellen Rudin, Peter J. Collins

Publication date: 1985

Full work available at URL: https://doi.org/10.2307/2045241

zbMATH Keywords

monotone normalityparacompactnessmetrizabilityNagata spacefirst countabilitysemimetricstratifiability

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (54D15)

Related Items (31)

A study on \(D\)-spaces and the metrizability of compact spaces with property (\(\sigma \)-A) ⋮ Concerning the Dugundji extension property ⋮ Mal'tsev spaces, retral spaces and rectifiable diagonals ⋮ More about Collins-Roscoe property in function spaces ⋮ The NZ property and \(D\)-spaces ⋮ On weaker forms of the chain \((F)\) condition and metacompactness-like covering properties in the product spaces ⋮ Existence of nice weak bases implies the \(D\)-property ⋮ The Collins-Roscoe property and its applications in the theory of function spaces ⋮ Monotonically monolithic spaces, Corson compacts, and \(D\)-spaces ⋮ Notes on the Collins-Roscoe property and \(D\)-spaces ⋮ Well-ordered (F) spaces are \(D\)-spaces ⋮ SOME WEAKER FORMS OF THE CHAIN (F) CONDITION FOR METACOMPACTNESS ⋮ Predictable network, monotonic monolithicity and \(D\)-spaces ⋮ Unnamed Item ⋮ The Collins-Roscoe mechanism and \(D\)-spaces ⋮ Monotone normality ⋮ The Collins-Roscoe structuring mechanism, \(D\)-spaces and related topics ⋮ Topological Spaces with Point-Networks ⋮ Some sufficiency conditions for \(D\)-spaces, dually discrete and its applications ⋮ A note concerning the Collins, Reed, Roscoe, Rudin metrization theorem ⋮ A note on proto-metrisable spaces ⋮ A note on the point-countable base question ⋮ A construction that yields a nonacyclic monotonically normal space ⋮ Acyclic monotone normality ⋮ A new approach to metrization ⋮ Open problems left in my wake of research ⋮ Monotonically normal $e$-separable spaces may not be perfect ⋮ Unnamed Item ⋮ Another View of Metrizability ⋮ Sequential characterizations of metrizability ⋮ Peter and Mike

Cites Work

• Unnamed Item
• A relation between perfect separability, completeness, and normality in semi-metric spaces
• Criteria for Metrisability
• Topological Spaces with Point-Networks
• The product of a normal space and a metric space need not be normal
• Metrization of Topological Spaces
• Point-Finite And Locally Finite Coverings
• Paracompactness and Strong Screenability

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