Euclidean convexity cannot be compactified

DOI10.1007/BF01456069zbMath0489.54021MaRDI QIDQ1166797

Marcel van de Vel

Publication date: 1983

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163726

zbMATH Keywords

convex structureseparation propertyEuclidean n-spaceconnected convex setscontinuous hull operatorextension of convexity to uniform compactificationtotally bounded uniformityuniform completions

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Axiomatic and generalized convexity (52A01) Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Dimension theory in general topology (54F45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (1)

Kakutani property of the polytopes implies Kakutani property of the whole space

Cites Work

• Axiomatic convexity theory and relationships between the Carathéodory, Helly, and Radon numbers
• Equality of the Lebesgue and the inductive dimension functions for compact spaces with a uniform convexity
• A Selection Theorem for Topological Convex Structures
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