2014/07/08 by Luis Montejano, Montejano, Luis
Computer Science · Mathematics · #52A35 #55N10 #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Metric Geometry (math.MG) #Topological and Geometric Data Analysis #math.MG #msc:52A35 #msc:55N10
paper · pdf · doi:10.48550/arxiv.1407.1947
arxiv created 2014/07/08 · openalex publication_date 2014/07/08 · arxiv updated 2014/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that for a topological space X with the property that Hp(U)=0 for p≥ 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≤ j ≤ 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.