- 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
- Files:
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(pdf, 153.4kb)
-
- Publisher copy:
- 10.1016/j.topol.2009.05.002
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- 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
- Language:
- English
- Keywords:
- Subjects:
- Copyright holder:
- Elsevier B.V.
- Copyright date:
- 2009
- Notes:
- Copyright 2009 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/
Journal article
On affine groups admitting invariant two-point sets
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