Geodesic
A compactness lemma for convex plane sets
Eurasian mathematical journal, Tome 2 (2011) no. 3, pp. 147-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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Given a closed bounded convex plane set covered by a family of open sets, we show that there is a finite dissection of the convex set into convex subsets, each of which lies within some open set of the covering. 
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     author = {M. N. Huxley},
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M. N. Huxley. A compactness lemma for convex plane sets. Eurasian mathematical journal, Tome 2 (2011) no. 3, pp. 147-149. http://geodesic.mathdoc.fr/item/EMJ_2011_2_3_a9/

[1] H. S. Hall, F. H. Stevens, A School Geometry, Macmillan, London, 1949

[2] M. N. Huxley, J. Žunić, “The number of configurations in lattice point counting. I”, Forum Mathematicum, 22 (2010), 127–152 | DOI | MR | Zbl