# Sh:1117

• Paolini, G., & Shelah, S. (2017). Group metrics for graph products of cyclic groups. Topology Appl., 232, 281–287.
• Abstract:
We complement the characterization of the graph products of cyclic groups G(\Gamma, {\mathfrak p}) admitting a Polish group topology of [9] with the following result. Let G = G(\Gamma, {\mathfrak p}), then the following are equivalent: [i] there is a metric on \Gamma which induces a separable topology in which E_{\Gamma} is closed; [ii] G(\Gamma, {\mathfrak p}) is embeddable into a Polish group; [iii] G(\Gamma, {\mathfrak p}) is embeddable into a non-Archimedean Polish group. We also construct left-invariant separable group ultrametrics for G = G(\Gamma, {\mathfrak p}) and \Gamma a closed graph on the Baire space, which is of independent interest.
• published version (7p)
Bib entry
@article{Sh:1117,
author = {Paolini, Gianluca and Shelah, Saharon},
title = {{Group metrics for graph products of cyclic groups}},
journal = {Topology Appl.},
fjournal = {Topology and its Applications},
volume = {232},
year = {2017},
pages = {281--287},
issn = {0166-8641},
doi = {10.1016/j.topol.2017.10.016},
mrclass = {54H11},
mrnumber = {3720899},
mrreviewer = {Michal Doucha},
doi = {10.1016/j.topol.2017.10.016},
note = {\href{https://arxiv.org/abs/1705.02582}{arXiv: 1705.02582}},
arxiv_number = {1705.02582}
}