Evenly distributed subsets of Sⁿ and a combinatorial application

Ky Fan

Vol. 98 (1982), No. 2, 323–325

DOI: 10.2140/pjm.1982.98.323

Abstract

A family ℱ of nonempty subsets of the n-sphere Sⁿ is said to be evenly distributed if every open hemisphere contains at least one set of ℱ. This paper first proves an antipodal theorem for evenly distributed families of nonempty closed subsets of Sⁿ, and then applies it to improve a recent combinatorial result of Kneser-Lovász-Bárány.

Mathematical Subject Classification 2000

Primary: 54H25

Secondary: 05C15

Milestones

Received: 15 April 1981

Published: 1 February 1982