We prove that for any non-degenerate continuum $K \subseteq \mathbb{R}^d$there exists a rectifiable curve such that its intersection with $K$ hasHausdorff dimension 1. This answers a question of B. Kirchheim.
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机译：我们证明，对于任何非退化的连续体$ K \ subseteq \ mathbb {R} ^ d $，都存在一条可校正的曲线，使得其与$ K $的交点具有Hausdorff维数1。这回答了B. Kirchheim的问题。
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