Geodesic
The metric space of Riemann surfaces over the sphere
Sbornik. Mathematics, Tome 82 (1995) no. 2, pp. 337-356 Cet article a éte moissonné depuis la source Math-Net.Ru

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The space of branched coverings of the Riemann sphere, augmented by degenerate elements (the points of the sphere), is given a metric compatible with kernel-convergence. 
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S. R. Nasyrov. The metric space of Riemann surfaces over the sphere. Sbornik. Mathematics, Tome 82 (1995) no. 2, pp. 337-356. http://geodesic.mathdoc.fr/item/SM_1995_82_2_a5/

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