Two new stories from the land of ultrafilter orders

Speaker(s)

Julia Ścisłowska

Affiliation

Doctoral School of Exact and Natural Sciences UW

Language of the talk

Polish

Date

Nov. 26, 2025, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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The main goal of the talk is to discuss two topics concerning ultrafilter orders on chainable continua: order type of ultrafilter orders on chainable continua and descriptive complexity of ultrafilter orders on chainable continua.
During my talk I will present known results about the order type of various chainable continua equipped with an ultrafilter order. In particular, I will discuss a theorem stating that any Suslinean chainable continuum equipped with any ultrafilter order has the order type of an interval.
Then I will present some results concerning descriptive complexity of ultrafilter orders on chainable continua. I will discuss the fact stating that the existence of a closed ultrafilter order characterizes the arc and the theorem that for Suslinean chainable continua, any ultrafilter order is both of type  F_{sigma} and G_{delta}. On the other hand, I will prove that there is no analytic and no co-analytic ultrafilter order on the Knaster continuum.
This is a joint work with Witold Marciszewski and Benjamin Vejnar, preprint is available at: https://arxiv.org/abs/2510.14577.

 

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