A topological transformation group without non-trivial equivariant compactifications
Dynamical Systems
2017-04-07 v3
Abstract
There is a countable metrizable group acting continuously on the space of rationals in such a way that the only equivariant compactification of the space is a singleton. This is obtained by a recursive application of a construction due to Megrelishvili, which is a metric fan equipped with a certain group of homeomorphisms. The question of existence of a topological transformation group with the property in the title was asked by Yu.M. Smirnov in the 1980s.
Cite
@article{arxiv.1601.03084,
title = {A topological transformation group without non-trivial equivariant compactifications},
author = {Vladimir G. Pestov},
journal= {arXiv preprint arXiv:1601.03084},
year = {2017}
}
Comments
17 pages, latex 2e. Minor revisions as requested by the Adv. Math. reviewer