Countable dense homogeneous semifilters

Prelegent(ci)

Lyubomyr Zdomskyy

Afiliacja

Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien

Język referatu

angielski

Termin

4 listopada 2026 16:15

Informacje na temat wydarzenia

This is an online talk. The link to the ZOOM seminar meeting will be sent later.

Seminarium

Seminarium „Topologia i teoria mnogości”

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A topological space is called countable dense homogeneous (CDH) if any two countable dense subsets can be mapped onto each other by a homeomorphism of the space onto itself. More than a decade ago, Hernández-Gutiérrez and Hrušák proved that every non-meager P-filter is CDH, and with  Kunen and Medini we have subsequently established the converse. The situation for semifilters remains considerably less understood, despite several results concerning their topological homogeneity. In particular, it is known that every Borel CDH semifilter is Polish and hence comeager. In this talk, we present a ZFC construction of a CDH semifilter that is not comeager. Since every CDH semifilter is non-meager, our example is neither meager nor comeager. We discuss this result in the context of the known characterizations of CDH filters and the broader problem of characterizing CDH semifilters.

The talk is going to be based on a joint work in progress with A. Medini.

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