KKM-type theorems for products of simplices and cutting sets and measures by straight lines
R.N. Karasev
TL;DR
This paper extends the KKM theorem to products of simplices and applies it to measure partition problems and set cutting in the plane, providing new theoretical insights and corollaries.
Contribution
It formulates a KKM-type theorem for products of simplices and derives new results for measure partitions and set cuts in the plane.
Findings
A version of the KKM theorem for products of simplices.
Corollaries for measure partition in the plane.
Results on cutting families of sets by 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.
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Taxonomy
TopicsMathematics and Applications · Data Management and Algorithms · Computational Geometry and Mesh Generation