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arXiv · 2302.06735

Homogeneous spaces not separated by arcs

Alexandre Karassev·Vesko Valov
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Abstract

It was shown by van Mill and Valov that regions in strongly locally homogeneous locally compact metric spaces of dimension $\ge 2$ are not separated by arcs. We improve this result by replacing strong local homogeneity with homogeneity. Moreover, we prove the result for the case when only one end point of an arc is in the interior of the region.

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Alexandre Karassev, Vesko Valov. 2023-02-13. Homogeneous spaces not separated by arcs. https://arxiv.org/abs/2302.06735

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