Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 1, pp. 133153 (2004) 

Unbounded regions in an arrangement of lines in the planeAlan WestSchool of Mathematics, University of Leeds, Leeds LS2 9JT, EnglandAbstract: We take a set $\Omega$ of $n$ points and an arrangement $\Sigma$ of $m$ lines in the plane which avoid these points but separate any two of them. We suppose these satisfy the following unboundedness property: for each point $x \in \Omega$ there is a homotopy from $\Sigma$ to ${\Sigma}'$ avoiding $\Omega$ so that $x$ is in an unbounded component of the complement of ${\Sigma}'$. It is proved that then $n \leq 2m$. This result is required to partially solve a problem in differential geometry which is described briefly. Full text of the article:
Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.
© 2004 Heldermann Verlag
