Large-volume open sets in normed spaces without integral distances

Sascha Kurz; Valery Mishkin

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Large-volume open sets in normed spaces without integral distances

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arxiv 1401.8174 v1 pith:ZBLZ57YZ submitted 2014-01-31 math.MG

Sascha Kurz , Valery Mishkin This is my paper · ORCID

classification math.MG

keywords integralsetsdistancesnormedopenspacesvolumeattaining

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abstract

We study open sets $\mathcal{P}$ in normed spaces $X$ attaining a large volume while avoiding pairs of points at integral distance. The proposed task is to find sharp inequalities for the maximum possible $d$-dimensional volume. This problem can be viewed as an opposite to known problems on point sets with pairwise integral or rational distances.

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