Dimensions of strong n-point sets |
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Authors: | John Cobb |
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Institution: | Mathematics Department, University of Idaho, Moscow, ID 83844-1103, USA |
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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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Keywords: | 54G99 54F45 |
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