Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 59, Number 2 (2018), 205-213.
Nonreduction of Relations in the Gromov Space to Polish Actions
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.
Notre Dame J. Formal Logic, Volume 59, Number 2 (2018), 205-213.
Received: 18 February 2015
Accepted: 5 October 2015
First available in Project Euclid: 8 January 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05] 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]
Secondary: 54H20: Topological dynamics [See also 28Dxx, 37Bxx] 54E50: Complete metric spaces
Álvarez López, Jesús A.; Candel, Alberto. Nonreduction of Relations in the Gromov Space to Polish Actions. Notre Dame J. Formal Logic 59 (2018), no. 2, 205--213. doi:10.1215/00294527-2017-0026. https://projecteuclid.org/euclid.ndjfl/1515402015