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.

翻译：本文探讨拓扑Helly型定理及其变体的最新进展。我们概述了两种不同的证明方法：一种基于神经引理，另一种基于不可嵌入性理论。