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## Main Question or Discussion Point

Suppose you know [itex]k_0A[/itex], for some set [itex]A \subset X[/itex] (where [itex]X[/itex] is a metric space) and some constant [itex]k_0[/itex], has nonempty interior. Do you then know that [itex]A[/itex] has nonempty interior, and/or that [itex]k A[/itex] has nonempty interior for

*any*constant [itex]k[/itex]?