Helly-type theorems for intersections of sets starshaped via orthogonally convex paths

Let be a family of simply connected sets in the plane. If every countable subfamily of has an intersection that is starshaped via orthogonally convex paths, then itself has such an intersection. For the d -dimensional case, let be a family of compact sets in . If every finite subfamily of has an int...

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Bibliographic Details
Published inAequationes mathematicae Vol. 84; no. 3; pp. 207 - 217
Main Author Breen, Marilyn
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.12.2012
Springer Nature B.V
Subjects
Analysis
Combinatorics
Intersections
Mathematical analysis
Mathematics
Mathematics and Statistics
Planes
Theorems
Sets starshaped via orthogonally convex paths
52.A35
52.A30
Online AccessGet full text
ISSN0001-9054
1420-8903
DOI10.1007/s00010-012-0151-0

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Summary:Let be a family of simply connected sets in the plane. If every countable subfamily of has an intersection that is starshaped via orthogonally convex paths, then itself has such an intersection. For the d -dimensional case, let be a family of compact sets in . If every finite subfamily of has an intersection that is starshaped via orthogonally convex paths, again itself has such an intersection.
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ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-012-0151-0