2010/10/11 by Dian Yang, Yang Dian, Yang, Dian
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Limits and Structures in Graph Theory #Metric Geometry (math.MG) #math.MG
paper · pdf · doi:10.48550/arxiv.1010.1990
2 pages, 1 figure, this note is one of the results of my participation in `Math in Moscow' program
arxiv created 2010/10/11 · openalex publication_date 2010/10/11 · arxiv updated 2010/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1933, Borsuk conjectured that any bounded d-dimensional set of nonzero diameter can be broken into d + 1 parts of smaller diameter. This conjecture was disproved for large enough d, though it is true for low dimensional cases. The paper provides an alternative proof for d = 2 case.