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Closed sets with the Kakeya property. (arXiv:1802.00286v1 [math.MG])
来源于:arXiv
We say that a planar set $A$ has the Kakeya property if there exist two
different positions of $A$ such that $A$ can be continuously moved from the
first position to the second within a set of arbitrarily small area. We prove
that if $A$ is closed and has the Kakeya property, then the union of the
nontrivial connected components of $A$ can be covered by a null set which is
either the union of parallel lines or the union of concentric circles. In
particular, if $A$ is closed, connected and has the Kakeya property, then $A$
can be covered by a line or a circle. 查看全文>>