On a transversal theorem of Montejano and Karasev
Andreas F. Holmsen

TL;DR
This paper presents a simplified proof of a theorem on $k$-dimensional transversals to convex sets, using the Borsuk-Ulam theorem, and extends the original result in some cases.
Contribution
A new, simpler proof of Montejano and Karasev's theorem employing the Borsuk-Ulam theorem, with potential improvements in specific cases.
Findings
Simplified proof of the original theorem.
Potentially stronger results in certain cases.
Application of the Borsuk-Ulam theorem to convex set transversals.
Abstract
We give a new proof of a theorem of Montejano and Karasev regarding -dimensional transversals to small families of convex sets. While their proof uses technical algebraic and topological tools, our proof is a simple application of the Borsuk-Ulam theorem. Additionally, in certain cases our result is stronger than the Montejano-Karasev theorem.
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Taxonomy
TopicsOptimization and Variational Analysis
