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López, Jesús A. Álvarez; Candel, Alberto

Nonreduction of relations in the Gromov space to Polish actions. (English) Zbl 1455.03061

Notre Dame J. Formal Logic 59, No. 2, 205-213 (2018).
Summary: We show that in the Gromov space of isometry classes of pointed proper metric spaces, the equivalence relations defined by existence of coarse quasi-isometries or being at finite Gromov-Hausdorff distance cannot be reduced to the equivalence relation defined by any Polish action.

MSC:

03E15 Descriptive set theory
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
54E50 Complete metric spaces

Keywords:

Gromov space; Gromov-Hausdorff metric; quasi-isometry
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\textit{J. A. Á. López} and \textit{A. Candel}, Notre Dame J. Formal Logic 59, No. 2, 205--213 (2018; Zbl 1455.03061)
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References:

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