A topological transformation group without non-trivial equivariant compactifications

作者：Pestov Vladimir G^*

来源：Advances in Mathematics, 2017, 311: 1-17.

DOI：10.1016/j.aim.2017.02.023

• Topological transformation group
• Equivariant compactification

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.

• 出版日期2017-4-30