Topology and Set Theory Seminar

Prelegent: **Damian Sobota**

2021-05-19 16:15

The starting point for my talk, based on the joint work with Piotr Borodulin-Nadzieja, is our theorem presented by him recently at this seminar, characterizing a special class of compact spaces without convergent sequences in the random model. Namely, we proved that if A is a Boolean algebra in the ground model V and M a measure algebra, then the Stone space of A has no non-trivial convergent sequences in the random extension V^M if and only if the family H(A,M) of all homomorphisms from A to M satisfies in V some special sequential property, expressed in terms of various topologies on H(A,M). During my talk I'll describe exactly those topologies, show some relations and differences between them, connect them with well-known topologies on spaces of measures, as well as state formally the aforementioned property and present the relation between the theorem and the famous Efimov problem.

2021-05-12