Critical ideals for compact spaces and Borel complexity of sets of ideal limit points

Speaker(s)

Rafał Filipów

Affiliation

Rafał Filipów

Language of the talk

English

Date

May 7, 2025, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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In the first part of my talk, I will introduce an ideal conv_alpha and use it to characterize (with the aid of the Katetov order) the class of all compact countable spaces which are homeomorphic to the space omega^alpha \cdot n + 1 with the order topology. In the second part, I will characterize ideals for which the family of all closed (F-sigma, resp.) sets of a space X coincides with a family of all sets of ideal limit points of sequences in X.  The above results are from joint works with M. Kowalczuk, A. Kwela and P. Leonetti (available at arXiv:2503.12571 and arXiv:2411.10866).

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