KKM-type theorems for products of simplices and cutting sets and measures by straight lines

Abstract

In this paper a version of Knaster-Kuratowski-Mazurkiewicz theorem for products of simplices is formulated. Some corollaries for measure partition in the plane and cutting families of sets in the plane by lines are given.

This paper was not accepted for publication in a journal. The referee considered the main topological lemma known. Though some corollaries may be of value, so this paper is posted to arxiv.org