A Helly-type theorem for intersections of certain orthogonal polytopes starshaped via \(k\)-staircase paths

DOI10.1007/s13366-020-00496-6zbMath1453.52007OpenAlexW3014368623MaRDI QIDQ2204387

Marilyn Breen

Publication date: 15 October 2020

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13366-020-00496-6

zbMATH Keywords

Helly-type theoremorthogonal polytopestarshaped via \(k\)-staircase paths

Mathematics Subject Classification ID

Helly-type theorems and geometric transversal theory (52A35) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Cites Work

• On staircase starshapedness in rectilinear spaces
• An improved Krasnosel'skij type theorem for orthogonal polygons which are starshaped via staircase paths
• A Helly theorem for intersections of orthogonally starshaped sets
• The Helly theorem for star-shaped sets
• A Krasnosel'skii-type theorem for certain orthogonal polytopes starshaped via \(k\)-staircase paths
• A Helly-type theorem for intersections of orthogonally starshaped sets in \(\mathbb R^d\)
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