Ordering metric spaces and Assouad Nagata dimension
Ordering metric spaces and Assouad Nagata dimension
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Anna Erschler, 脡cole Normale Sup茅rieure
We show that all spaces of finite Assouad-Nagata dimension admit听a good order for Travelling Salesman Problem, and provide sufficient听conditions under听which the converse is true (joint with I. Mitrofanov). One of such conditions can be described in听terms of a spectral gap for a sequence of graphs, and another one is the听property of containing weakly cubes of arbitrary large dimension.听We discuss then spaces which admits extremely good ordering (as good as听for metric trees).