Abelian pro-countable groups and orbit equivalence relations

• Autorzy: Maciej Malicki
• Języki publikacji: EN

Abstrakty

EN

We study a class of abelian groups that can be defined as Polish pro-countable groups, as non-archimedean groups with a compatible two-sided invariant metric or as quasi-countable groups, i.e., closed subdirect products of countable discrete groups, endowed with the product topology.
We show that for every non-locally compact, abelian quasi-countable group G there exists a closed L ≤ G and a closed, non-locally compact K ≤ G/L which is a direct product of discrete countable groups. As an application we prove that for every abelian Polish group G of the form H/L, where H,L ≤ Iso(X) and X is a locally compact separable metric space (in particular, for every abelian, quasi-countable group G), the following holds: G is locally compact iff every continuous action of G on a Polish space Y induces an orbit equivalence relation that is reducible to an equivalence relation with countable classes.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 54H11: Topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 233
• Numer: 1
• Strony: 83-99

Daty

wydano

2016

Twórcy

autor

Maciej Malicki

• Department of Mathematics and Mathematical Economics, Warsaw School of Economics, al. Niepodległości 162, 02-554 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm987-1-2016