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- W4287163982 abstract "For $nleq d$, a family ${cal F}={C_0,C_1,ldots, C_n}$ of compact convex sets in $R^d$ is called an $n$-critical family provided any $n$ members of ${cal F}$ have a non-empty intersection, but $bigcap_{i=0}^n C_i=varnothing$. If $n=d$ then a lemma on the intersection of convex sets due to Klee implies that the $d+1$ members of the $d$-critical family enclose a `hollow' in $R^d$, a bounded connected component of $R^dsetminusbigcup_{i=0}^n C_i.$ Here we prove that the closure of the convex hull of a hollow in $R^d$ is a $d$-simplex." @default.
- W4287163982 created "2022-07-25" @default.
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- W4287163982 date "2021-05-29" @default.
- W4287163982 modified "2023-10-17" @default.
- W4287163982 title "On the hollow enclosed by convex sets" @default.
- W4287163982 doi "https://doi.org/10.48550/arxiv.2105.14306" @default.
- W4287163982 hasPublicationYear "2021" @default.
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