Hilbert-geometry covering numbers satisfy polarity duality: N^H_K(G, α) is bounded above and below by c^{±d} times N^H_{G°}(K°, α) for an absolute constant c.
Artstein-Avidan, A
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On the Duality of Coverings in Hilbert Geometry
Hilbert-geometry covering numbers satisfy polarity duality: N^H_K(G, α) is bounded above and below by c^{±d} times N^H_{G°}(K°, α) for an absolute constant c.