A space \(C_p(X)\) is dominated by irrationals if and only if it is \(K\)-analytic
From MaRDI portal
Publication:2387164
DOI10.1007/S10474-005-0194-YzbMath1081.54012OpenAlexW1984986733MaRDI QIDQ2387164
Publication date: 26 January 2006
Published in: Acta Mathematica Hungarica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10474-005-0194-y
\(K\)-analytic spaceHewitt realcompactificationdomination by irrationalspointwise convergence topolgystrong domination by irrationals
Continuous maps (54C05) Function spaces in general topology (54C35) Compactness (54D30) Product spaces in general topology (54B10)
Related Items (41)
If \(C_{p}(X)\) is strongly dominated by a second countable space, then \(X\) is countable ⋮ A characterization of the existence of a fundamental bounded resolution for the space \(C_c(X)\) in terms of \(X\) ⋮ A selection of recent results and problems in \(C_{p}\)-theory ⋮ Compact spaces with a \(\mathbb{P}\)-diagonal ⋮ \(\omega^\omega\)-dominated function spaces and \(\omega^{\omega}\)-bases in free objects of topological algebra ⋮ Resolutions of topological linear spaces and continuity of linear maps ⋮ Valdivia's lifting theorem for non-metrizable spaces ⋮ Covering properties of Cp(X) and Ck(X) ⋮ Strong domination by countable and second countable spaces ⋮ Metrizable-like locally convex topologies on \(C(X)\) ⋮ Descriptive topology for analysts ⋮ Two new properties of the space \(C_{p}(x)\) ⋮ Unnamed Item ⋮ Domination by metric spaces ⋮ Compact coverings for Baire locally convex spaces ⋮ Domination by second countable spaces and Lindelöf \(\Sigma \)-property ⋮ The number of \(K\)-determination of topological spaces ⋮ Unnamed Item ⋮ Lindelöf spaces C(X) over topological groups ⋮ Some criteria for \(C_p(X)\) to be an \(L\Sigma(\leq\omega)\)-space ⋮ Existence of nice resolutions in \(C_p(X)\) and its bidual often implies metrizability of \(C_p(X)\) ⋮ A NOTE ON SPACES Cp(X)K-ANALYTIC-FRAMED IN ℝX ⋮ The strong Pytkeev property for topological groups and topological vector spaces ⋮ On topological properties of Fréchet locally convex spaces with the weak topology ⋮ A note on paratopological groups with an \(\omega^\omega \)-base ⋮ Web-compact spaces, Fréchet-Urysohn groups and a Suslin closed graph theorem ⋮ On quasi-Souslin \(C_{c}(X)\) spaces ⋮ Some applications of discrete selectivity and Banakh property in function spaces ⋮ Free locally convex spaces with a small base ⋮ On realcompact topological vector spaces ⋮ On topological groups with a small base and metrizability ⋮ Compact covers and function spaces ⋮ A note on a theorem of Talagrand ⋮ A revised closed graph theorem for quasi-Suslin spaces ⋮ Some characterizations for \(\upsilon X\) to be Lindelöf \(\Sigma \) or \(K\)-analytic in terms of \(C_{p}(X)\) ⋮ Spaces with an \(M\)-diagonal ⋮ Calibers, \(\omega\)-continuous maps and function spaces ⋮ Some results on separate and joint continuity ⋮ DOMINATION CONDITIONS UNDER WHICH A COMPACT SPACE IS METRISABLE ⋮ Unnamed Item ⋮ Two Classes of Metrizable Spaces $$\ell _{c}$$-Invariant
This page was built for publication: A space \(C_p(X)\) is dominated by irrationals if and only if it is \(K\)-analytic