Continuous functions on totally ordered spaces that are compact in their order topologies

DOI10.1006/jfan.2000.3652zbMath1003.46002OpenAlexW2015701201MaRDI QIDQ1840770

J. E. Jayne, C. A. Rogers, Isaac Namioka, Richard Haydon

Publication date: 30 January 2003

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2000.3652

zbMATH Keywords

order topologytotally ordered spacelower-semicontinuousequivalent locally uniformly convex normequivalent Kadec norm

Mathematics Subject Classification ID

Isomorphic theory (including renorming) of Banach spaces (46B03) Ordered topological linear spaces, vector lattices (46A40) Ordered normed spaces (46B40)

Related Items (13)

Metrization theory and the Kadec property ⋮ Linearly ordered compacta and Banach spaces with a projectional resolution of the identity ⋮ Upper Namioka property of compact-valued mappings ⋮ An application of Mary Ellen Rudin's solution to Nikiel's conjecture ⋮ Topological properties of the continuous function spaces on some ordered compacta ⋮ Locally uniformly rotund renormings of the spaces of continuous functions on Fedorchuk compacts ⋮ Sequentially compact subsets and monotone functions: an application to fuzzy theory ⋮ Fragmentability in Banach spaces: interaction of topologies ⋮ Renormings of \(C(K)\) spaces ⋮ On Banach spaces whose norm-open sets are \(F_\sigma \)-sets in the weak topology ⋮ On surjections between Banach spaces of continuous functions on separable nonmetrizable compact lines ⋮ Lexicographic products as compact spaces of the first Baire class ⋮ Borel measurability of separately continuous functions

Cites Work

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• On a property of the norm which is close to locally uniform rotundity
• On dual locally uniformly rotund norms
• Continuous functions on compact totally ordered spaces
• Locally uniformly rotund renorming and decompositions of Banach spaces
• Trees in Renorming Theory
• Continuous functions on products of compact Hausdorff spaces

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