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| Format: | Preprint |
| Published: |
2012
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1210.2050 |
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Table of Contents:
- If $ϕ: L\to L'$ is a bijection from the set of lines of a linear space $(P,L)$ onto the set of lines of a linear space $(P',L')$ ($\dim P, \dim P'\geq 3$), such that intersecting lines go over to intersecting lines in both directions, then $ϕ$ is arising from a collineation of $(P,L)$ onto $(P',L')$ or a collineation of $(P,L)$ onto the dual linear space of $(P',L')$. However, the second possibility can only occur when $(P,L)$ and $(P',L')$ are 3-dimensional generalized projective spaces.