On affine groups admitting invariant two-point sets
A two-point set is a subset of the plane which meets every line in exactly two points. We discuss previous work on the topological symmetries of a two-point set, and show that there exist subgroups of S<sup>1</sup> which do not leave any two-point set invariant. Further, we show that two...
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
Elsevier
2009
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| Témata: |
| Shrnutí: | A two-point set is a subset of the plane which meets every line in exactly two points. We discuss previous work on the topological symmetries of a two-point set, and show that there exist subgroups of S<sup>1</sup> which do not leave any two-point set invariant. Further, we show that two-point sets may be chosen to be topological groups, in which case they are also homogeneous. |
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