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arXiv · 1407.1947

A New Topological Helly Theorem and some Transversals Results

Luis Montejano
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Abstract

We prove that for a topological space X with the property that $H_p(U)=0$ for $p\geq d$ and every open subset $U$ of $X$, a finite family of open sets in $X$ has nonempty intersection if for any subfamily of size $j$, $1\leq j \leq d+1$, the $(d-j)$-dimensional homology group of its intersection is zero. We use this theorem to prove new results concerning transversal affine planes to families of convex sets.

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Luis Montejano. 2014-07-08. A New Topological Helly Theorem and some Transversals Results. https://arxiv.org/abs/1407.1947

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