A topological proof of Ky Fan's covering lemma

2025/07/29 by Chornomaz, Bogdan
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.22184

Abstract

We give an intuitive combinatorial proof of Ky Fan's covering lemma based on the Borsuk-Ulam theorem. We then show how this approach can be generalized to Ky Fan's covering lemma for several linear orders.

Citations

• Local Borsuk-Ulam, Stability, and Replicability
• Oriented matroids and Ky Fan's theorem
• The Borsuk-Ulam-property, Tucker-property and constructive proofs in combinatorics
• Local chromatic number, Ky Fan's theorem, and circular colorings

Related

• Ky Fan theorem for sphere bundles
• Covering and labeling generalizations of the Borsuk-Ulam theorem
• A Combinatorial Analog of a Theorem of F.J.Dyson
• Colorful Borsuk--Ulam theorems and applications
• On a generalization of Kelly's combinatorial lemma