In this note we prove that for any compact subset S of a Busemann surface
(S,d) (in particular, for any simple polygon with geodesic metric)
and any positive number δ, the minimum number of closed balls of radius
δ with centers at S and covering the set S is at most 19
times the maximum number of disjoint closed balls of radius δ centered
at points of S: ν(S)≤ρ(S)≤19ν(S), where ρ(S) and
ν(S) are the covering and the packing numbers of S by δ-balls.Comment: 27 page