Unbounded Regions in an Arrangement of Lines in the Plane
نویسندگان
چکیده
We take a set Ω of n points and an arrangement Σ 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 ∈ Ω there is a homotopy from Σ to Σ′ avoiding Ω so that x is in an unbounded component of the complement of Σ′. It is proved that then n ≤ 2m. This result is required to partially solve a problem in differential geometry which is described briefly.
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