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For every affine variety over a global function field, we show that the setof its points with coordinates in an arbitrary rank-one multiplicative subgroupof this function field is topologically dense in the set of its points withcoordinates in the topological closure of this subgroup in the product of themultiplicative group of those local completions of this function field over allbut finitely many places.

A Local-Global Equality on Every Affine Variety Admitting Points in an Arbitrary Rank-One Subgroup of a Global Function Field