Helly-type problems from a topological perspective
Pavel Pat\'ak, Zuzana Pat\'akov\'a
TL;DR
This paper reviews recent advances in topological Helly-type theorems, highlighting two proof techniques—nerve lemma and non-embeddability—contributing to the understanding of their variants.
Contribution
It offers a comparative overview of proof methods for topological Helly-type theorems, emphasizing their recent developments and applications.
Findings
Two proof techniques for Helly-type theorems are discussed
Recent progress has been made in topological variants of Helly's theorem
The paper highlights the significance of nerve lemma and non-embeddability methods
Abstract
We discuss recent progress on topological Helly-type theorems and their variants. We provide an overview of two different proof techniques, one based on the nerve lemma, while the other on non-embeddability.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows