A critical ideal with respect to Mazurkiewicz's theorem in terms of the Katetov order

Speaker(s)

Rafał Filipów

Affiliation

The University of Gdańsk

Language of the talk

English

Date

Nov. 25, 2015, 4:15 p.m.

Room

room 5050

Title in Polish

A critical ideal with respect to Mazurkiewicz's theorem in terms of the Katetov order

Seminar

Topology and Set Theory Seminar

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Consider a property of ideals: property(I). One can ask whether there is a critical ideal C for property(I) in terms of the Katetov order <_K i.e. property(I) <=> C <_K I. Many examples of critical ideals for various properties can be found in Hrusak's paper ``Combinatorics of filters and ideals''. In the first part of my talk I show a few examples of properties of ideals and critical ideals for these properties in the Katetov order. In the second part I show a critical ideal with respect to Mazurkiewicz's theorem. At the end I show a relationship between Part 2 and a question of Hrusak about extendability of ideals to F_sigma ideals. A theorem of Mazurkiewicz I'm going to talk about says that for every bounded sequence of continuous functions f_n:R->R there is a perfect set P such that the sequence (f_n|P) has a pointwise convergent subsequence.

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