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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| Format: | Journal article |
| Language: | English |
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Elsevier
2009
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| _version_ | 1826281981105668096 |
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| author | Chad, B Suabedissen, R |
| author_facet | Chad, B Suabedissen, R |
| author_sort | Chad, B |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T00:36:59Z |
| format | Journal article |
| id | oxford-uuid:81c0b813-086b-4cb0-8646-b91fd31fd03a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:36:59Z |
| publishDate | 2009 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:81c0b813-086b-4cb0-8646-b91fd31fd03a2022-03-26T21:32:23ZOn affine groups admitting invariant two-point setsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:81c0b813-086b-4cb0-8646-b91fd31fd03aAnalytic Topology or TopologyAlgebraic topologyEnglishOxford University Research Archive - ValetElsevier2009Chad, BSuabedissen, RA 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. |
| spellingShingle | Analytic Topology or Topology Algebraic topology Chad, B Suabedissen, R On affine groups admitting invariant two-point sets |
| title | On affine groups admitting invariant two-point sets |
| title_full | On affine groups admitting invariant two-point sets |
| title_fullStr | On affine groups admitting invariant two-point sets |
| title_full_unstemmed | On affine groups admitting invariant two-point sets |
| title_short | On affine groups admitting invariant two-point sets |
| title_sort | on affine groups admitting invariant two point sets |
| topic | Analytic Topology or Topology Algebraic topology |
| work_keys_str_mv | AT chadb onaffinegroupsadmittinginvarianttwopointsets AT suabedissenr onaffinegroupsadmittinginvarianttwopointsets |