Recent Research on Effros theorem part2(Machine Learning 2024)
- On the scope of the Effros theorem(arXiv)
Author : Andrea Medini
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: under AC, there exists a non-Effros group; under AD, every group is Effros; under V=L, there exists a coanalytic non-Effros group. The above counterexamples will be graphs of discontinuous homomorphisms.
2. The Feldman-Moore, Glimm-Effros, and Lusin-Novikov theorems over quotients(arXiv)
Author : N. de Rancourt, B. D. Miller
Abstract : We establish generalizations of the Feldman-Moore theorem, the Glimm-Effros dichotomy, and the Lusin-Novikov uniformization theorem from Polish spaces to their quotients by Borel orbit equivalence relations.
