In the Cantor-space topology, generic subsets of the nonnegative integers are not Bh[g] sets and have maximally wild representation functions, while finite subsets of vector spaces are generically Bh[g].
Leonetti, Almost all sets of nonnegative integers and their small perturbations are not sumsets, Proc
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In the Cantor-space topology, generic subsets of the nonnegative integers are not Bh[g] sets and have maximally wild representation functions, while finite subsets of vector spaces are generically Bh[g].