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respectively. When this is not specified, the barrier is assumed to have no constraints on its location. Versions of the problem in which the opaque set must be connected or form a single curve have also been considered. It is not known whether every convex set has a shortest opaque set, or whether instead the lengths of its opaque sets might approach an infimum without ever reaching it. Every opaque set for can be approximated arbitrarily closely in length by an opaque forest,

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