This article is cited in 6 papers

Theorems of Borsuk-Ulam type for flats and common transversals of families of convex compact sets

R. N. Karasev

Moscow Institute of Physics and Technology

Abstract: Several results on the topology of the space of $k$-flats in $\mathbb R^n$ similar to the Borsuk-Ulam theorem on coverings of a sphere and a ball are proved. Some corollaries on common transversals for families of subsets of $\mathbb R^n$ and on measure partitions by hyperplanes are deduced.
Bibliography: 22 titles.

Keywords: Borsuk-Ulam theorem, common transversals, Helly-type theorems.

UDC: 514.17+514.172

MSC: 52A35, 55M30, 55M35

Received: 05.06.2008 and 30.06.2009

DOI: 10.4213/sm6376

 English version: Sbornik: Mathematics, 2009, 200:10, 1453–1471

Bibliographic databases:

• 
• 
• 
• 
• 
• 
•