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On affine groups admitting invariant two-point sets

Abstract:
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 S1 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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1016/j.topol.2009.05.002

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Institution:
University of Oxford
Oxford college:
St Edmund Hall
Department:
Mathematical,Physical & Life Sciences Division - Mathematical Institute
More by this author
Institution:
University of Oxford
Oxford college:
Lady Margaret Hall
Department:
Mathematical,Physical & Life Sciences Division
Publisher:
Elsevier Inc.
Journal:
Topology and its Applications Journal website
Volume:
156
Issue:
13
Pages:
2209–2213
Publication date:
2009-08-05
DOI:
ISSN:
0166-8641
URN:
uuid:81c0b813-086b-4cb0-8646-b91fd31fd03a
Local pid:
ora:10775

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