TOPOLOGICAL ISOMORPHISM FOR RANK-1 SYSTEMS

@inproceedings{Hill2013TOPOLOGICALIF,
  title={TOPOLOGICAL ISOMORPHISM FOR RANK-1 SYSTEMS},
  author={Aaron Hill},
  year={2013}
}
We define the Polish space R of non-degenerate rank-1 systems. Each non-degenerate rank-1 system can be viewed as a measurepreserving 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 Fσ as a subset of R × R and bi-reducible to E0. We also explicitly describe… CONTINUE READING

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