Limits of topological minimal sets with finitely generated coefficient groups

Abstract

We prove that Hausdorff limit of topological minimal sets (with finitely generated coefficient group) are topologically minimal. The key idea is to reduce the homology group on the space to the homology group on the sphere, and 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.