Inventiones mathematicae

, Volume 197, Issue 2, pp 433–452 | Cite as

True trees are dense

  • Christopher J. Bishop


We show that any compact, connected set K in the plane can be approximated by the critical points of a polynomial with two critical values. Equivalently, K can be approximated in the Hausdorff metric by a true tree in the sense of Grothendieck’s dessins d’enfants.

Mathematics Subject Classification



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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Mathematics DepartmentStony Brook UniversityStony BrookUSA

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