Strictly convex norms, $G_{𝛿}$-diagonals and non-Gruenhage spaces

DOI10.1090/S0002-9939-2012-11142-6zbMath1282.46015OpenAlexW2093433263MaRDI QIDQ2845736

Richard J. Smith

Publication date: 3 September 2013

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-2012-11142-6

zbMATH Keywords

\(G_\delta\)-diagonalstrictly convex normGruenhage spacesmooth bump functionproperty \((\ast)\), ZFC

Mathematics Subject Classification ID

Isomorphic theory (including renorming) of Banach spaces (46B03) Banach spaces of continuous, differentiable or analytic functions (46E15) Scattered spaces (54G12)

Related Items (4)

CHAINS OF FUNCTIONS IN -SPACES ⋮ On Gruenhage spaces, separating \(\sigma\)-isolated families, and their relatives ⋮ Compact convex sets that admit a lower semicontinuous strictly convex function ⋮ A topological characterization of dual strict convexity in Asplund spaces

Cites Work

• Renormings of \(C(K)\) spaces
• Gruenhage compacta and strictly convex dual norms
• Strictly convex norms and topology
• SMOOTH NORMS AND APPROXIMATION IN BANACH SPACES OF THE TYPE 𝒞(K)
• A Note on Gul'ko Compact Spaces
• Trees in Renorming Theory
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