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Illumination for unions of boxes in $\textbf {R}^ d$


Author: Marilyn Breen
Journal: Proc. Amer. Math. Soc. 116 (1992), 197-202
MSC: Primary 52A30
DOI: https://doi.org/10.1090/S0002-9939-1992-1089402-6
MathSciNet review: 1089402
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Abstract: Let $S$ be a finite union of boxes (polytopes whose edges are parallel to the coordinate axes) in ${R^d}$. If every two vertices of $S$ are clearly illumined by some common translate of the box $T$, then there is a translate of $T$ that clearly illumines every point of $S$ . A similar result holds when appropriate boundary points of $S$ are illumined (rather than clearly illumined) by translates of box $T$.


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Article copyright: © Copyright 1992 American Mathematical Society