Metrizability vs. Fréchet-Uryshon property

DOI10.1090/S0002-9939-03-06944-2zbMath1044.46001MaRDI QIDQ4417268

Jerzy Kąkol, Stephen A. Saxon, Bernardo Cascales

Publication date: 28 July 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

locally convex spacetopology of pointwise convergencecountable tightnessmetrizabilityFréchet-Urysohn propertycountable bounded tightness

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Metric spaces, metrizability (54E35) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Uniform structures and generalizations (54E15) General theory of locally convex spaces (46A03) Locally convex Fréchet spaces and (DF)-spaces (46A04) Barrelled spaces, bornological spaces (46A08) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

Related Items (24)

On countable bounded tightness for spaces \(C_{p}(X)\) ⋮ Bounded tightness for locally convex spaces and spaces \(C(X)\) ⋮ Spaces \(C(X)\) with ordered bases ⋮ Tightness and distinguished Fréchet spaces ⋮ A class of angelic sequential non-Fréchet--Urysohn topological groups ⋮ Valdivia's lifting theorem for non-metrizable spaces ⋮ Compact coverings for Baire locally convex spaces ⋮ Some topological cardinal inequalities for spaces \(C_p(X)\) ⋮ Power bounded composition operators on spaces of analytic functions ⋮ A NOTE ON SPACES C_p(X)K-ANALYTIC-FRAMED IN ℝ^X ⋮ The strong Pytkeev property for topological groups and topological vector spaces ⋮ On topological properties of Fréchet locally convex spaces with the weak topology ⋮ Quasi-Suslin weak duals ⋮ Topological properties of inductive limits of closed towers of metrizable groups ⋮ On realcompact topological vector spaces ⋮ On a three-space property for Lindelöf \(\Sigma\)-spaces, (WCG)-spaces and the Sobczyk property ⋮ On metrizability of compactoid sets in non-archimedean locally convex spaces ⋮ The dual of the locally convex space \(C_p(X)\) ⋮ Necessary and sufficient conditions for precompact sets to be metrisable ⋮ The quotient/codimension problems ⋮ If not distinguished, is $C_{p}( X) $ even close? ⋮ Weakly K-analytic spaces and the three-space property for analyticity ⋮ NOTE ABOUT LINDELÖF Σ-SPACES υX ⋮ On topological spaces and topological groups with certain local countable networks

Cites Work

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• Montel (DF)-Spaces, Sequential (LM)-Spaces and the Strongest Locally Convex Topology
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