Orbitwise topologies and quasi-Polish techniques for Polish group actions

Speaker(s)

Ruiyuan Chen

Affiliation

University of Warsaw

Language of the talk

Polish

Date

March 25, 2026, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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Given a Polish group G with a Borel action on X, the group topology on G induces a canonical quotient topology on each orbit; we call the disjoint union of these the orbitwise topology on X. Fundamental results of Effros, Pettis, and Becker–Kechris (among others) show that the orbitwise topology is a canonical structure which "determines" all the topological information that is contained already in the Borel sigma-algebra.
In this talk, we will present a new proof of the Becker–Kechris theorem that emphasizes this perspective, from a 2024 paper (arXiv:2209.06319). A prominent role in this proof is played by M. de Brecht's quasi-Polish spaces (2013), which allow and encourage reasoning about Polish topologies as algebraic structures; we will give an introduction to quasi-Polish spaces as part of the talk.

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