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arXiv · 2109.12181

Assouad-Nagata dimension and gap for ordered metric spaces

Anna Erschler·Ivan Mitrofanov
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Abstract

We prove that all spaces of finite Assouad-Nagata dimension admit a good order for Travelling Salesman Problem, and provide sufficient conditions under which the converse is true. We formulate a conjectural characterisation of spaces of finite $AN$-dimension, which would yield a gap statement for the efficiency of orders on metric spaces. Under assumption of doubling, we prove a stronger gap phenomenon about all orders on a given metric space.

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Anna Erschler, Ivan Mitrofanov. 2021-09-24. Assouad-Nagata dimension and gap for ordered metric spaces. https://arxiv.org/abs/2109.12181

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