n-point sets and graphs of functions |
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Authors: | John Cobb |
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Institution: | Department of Mathematics, University of Idaho, Moscow, ID 83844-1103, USA |
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Abstract: | We prove that, for every n?2, there exists an n-point set (a plane set which hits every line in exactly n points) that is homeomorphic to the graph of a function from R to R; for n?4, there exist both 0-dimensional and 1-dimensional examples. This raises the question (which we do not answer) of whether n-point sets for different n's could be homeomorphic. |
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Keywords: | 54G99 54G15 54G20 54F50 |
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