Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661544 | Topology and its Applications | 2006 | 7 Pages |
Abstract
n-point sets (plane sets which hit each line in n points) and strong n-point sets (in addition hit each circle in n-points) exist (for n⩾2, n⩾3 respectively) by transfinite induction, but their properties otherwise are difficult to establish. Recently for n-point sets the question of their possible dimensions has been settled: 2- and 3-point sets are always zero-dimensional, while for n⩾4, one-dimensional n-point sets exist. We settle the same question for strong n-point sets: strong 4- and 5-point sets are always zero-dimensional, while for n⩾6, both zero-dimensional and one-dimensional strong n-point sets exist.
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Physical Sciences and Engineering
Mathematics
Geometry and Topology