Semiaffine stable planes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914970231373824 |
|---|---|
| author | Löwen, Rainer Stroppel, Markus Johannes |
| author_facet | Löwen, Rainer Stroppel, Markus Johannes |
| contents | A locally compact stable plane of positive topological dimension will be called semiaffine if for every line $L$ and every point $p$ not in $L$ there is at most one line passing through $p$ and disjoint from $L$. We show that then the plane is either an affine or projective plane or a punctured projective plane (i.e., a projective plane with one point deleted). We also compare this with the situation in general linear spaces (without topology), where P. Dembowski showed that the analogue of our main result is true for finite spaces but fails in general. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00360 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semiaffine stable planes Löwen, Rainer Stroppel, Markus Johannes Geometric Topology 51H10, 51M30 A locally compact stable plane of positive topological dimension will be called semiaffine if for every line $L$ and every point $p$ not in $L$ there is at most one line passing through $p$ and disjoint from $L$. We show that then the plane is either an affine or projective plane or a punctured projective plane (i.e., a projective plane with one point deleted). We also compare this with the situation in general linear spaces (without topology), where P. Dembowski showed that the analogue of our main result is true for finite spaces but fails in general. |
| title | Semiaffine stable planes |
| topic | Geometric Topology 51H10, 51M30 |
| url | https://arxiv.org/abs/2309.00360 |