Abstract
We define the Polish space R of non-degenerate rank-1 systems. Each non-degenerate rank-1 system can be viewed as a measure-preserving transformation of an atomless, σ-finite measure space and as a homeomorphism of a Cantor space. We completely characterize when two non-degenerate rank-1 systems are topologically isomorphic. We also analyze the complexity of the topological isomorphism relation on R, showing that it is \({F_\sigma }\) as a subset of R× R and bi-reducible to E 0. We also explicitly describe when a non-degenerate rank-1 system is topologically isomorphic to its inverse.
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S. G. acknowledges the US NSF grants DMS-0901853 and DMS-1201290 for the support of his research.
A. H. acknowledges the US NSF grant DMS-0943870 for the support of his research.
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Gao, S., Hill, A. Topological isomorphism for rank-1 systems. JAMA 128, 1–49 (2016). https://doi.org/10.1007/s11854-016-0001-4
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DOI: https://doi.org/10.1007/s11854-016-0001-4