PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On the scope of the Effros theorem

Volume 258 / 2022

Andrea Medini Fundamenta Mathematicae 258 (2022), 211-223 MSC: Primary 54H11, 54H05; Secondary 22F05, 03E15, 03E45, 03E60. DOI: 10.4064/fm100-12-2021 Published online: 11 March 2022

Abstract

All spaces (and groups) are assumed to be separable and metrizable. Jan van Mill showed that every analytic group $G$ is Effros (that is, every continuous transitive action of $G$ on a non-meager space is micro-transitive). We complete the picture by obtaining the following results:
$\bullet $ under $\mathsf{AC}$, there exists a non-Effros group,
$\bullet $ under $\mathsf{AD} $, every group is Effros,
$\bullet $ under $\mathsf {V=L}$, there exists a coanalytic non-Effros group.
The above counterexamples will be graphs of discontinuous homomorphisms.

Authors

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image