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Limits of topological minimal sets with finitely generated coefficient groups

We prove that the (local) Hausdorff limit of topological minimal sets (with finitely generated coefficient group) is topologically minimal. The key idea is to reduce the homology group on the space to the homology group on the sphere, and then reduce the homology group on the sphere to a finitely representable one, by ‘glueing’ grids with small measure to block local elements in the homology group.