The ham sandwich theorem revisited

Abstract

This paper continues the search, started in [10], for relatives of the ham sandwich theorem. We prove among other results, the following implications {fx21-1} where K(n, k) is an important instance of the Knaster's conjecture so that K(n, n - 1) reduces to the Borsuk-Ulam theorem, B(n, k) is a R. Rado type statement about (k + 1) measures in R n where B(n, n - 1) turns out to be the ham sandwich theorem and C(n, k) is a topological statement, established in this paper in the case C(n, n - 2), n = 3 or n ≥ 5.