Illumination for unions of boxes in 𝑅^{𝑑}

Breen, Marilyn

doi:10.1090/S0002-9939-1992-1089402-6

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

Proc. Amer. Math. Soc. 116 (1992), 197-202

DOI: https://doi.org/10.1090/S0002-9939-1992-1089402-6

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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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