On two questions concerning tilings

DOI10.1007/BF02761301zbMath0780.52001OpenAlexW2090513347MaRDI QIDQ1261910

Mark J. Nielsen

Publication date: 7 September 1993

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02761301

zbMATH Keywords

Hilbert spaceBanach spacetopological diskconvex tiling

Mathematics Subject Classification ID

Combinatorial aspects of tessellation and tiling problems (05B45) Convex sets in topological vector spaces (aspects of convex geometry) (52A07) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Cites Work

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• A characterization theorem for tilings having countably many singular points
• Some tilings of the plane whose singular points are uncountable and unbounded
• Three characterizations of polyhedral Banach spaces
• Singular points of a star-finite tiling
• Tilings whose members have finitely many neighbors
• Locally countable plump tilings are flat
• Singular points of a convex tiling
• One property of Lindenstrauss-Phelps spaces
• Dispersed Chebyshev sets and coverings by balls
• Tilings of the plane by topological disks
• Extreme point properties of convex bodies in reflexive Banach spaces
• Some Tilings of the Plane Whose Singular Points Form a Perfect Set
• Collections of convex sets which cover a Banach space

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