2009/05/31 by R. N. Karasev, Roman N Karasev · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Holomorphic and Operator Theory #math.AT #math.CO #msc:52A35 #msc:55M30 #msc:55M35
paper · pdf · doi:10.1070/sm2009v200n10abeh004045
published as Math. Sbornik, 200:10, 2009, 39-58 · Corrected typos and added the journal reference
openalex publication_date 2009/10/31 · arxiv created 2009/11/25 · arxiv updated 2011/07/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper some results on the topology of the space of k-flats in \mathbb Rn are proved, similar to the Borsuk-Ulam theorem on coverings of sphere. Some corollaries on common transversals for families of compact sets in \mathbb Rn, and on measure partitions by hyperplanes, are deduced.