Every homeomorphism admitting a fully supported invariant measure can be approximated in the C^0-Gromov-Hausdorff topology by zero-entropy homeomorphisms.
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Invariant measures with full support and approximation by zero-entropy systems in the $C^0$-Gromov--Hausdorff topology
Every homeomorphism admitting a fully supported invariant measure can be approximated in the C^0-Gromov-Hausdorff topology by zero-entropy homeomorphisms.