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Tuesday, 17 March 2026 - 10:00 to 11:30 <br />
Place: IM, konírna
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Speaker: Jerzy Kąkol, A. Mickiewicz University, Poznań, Poland<br />
Title: On mysterious subsets of the real line and their applicable topological-algebraic counterparts
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Abstract <br />
<p>There has recently been quite an interest in the study of ∆-spaces, i.e. spaces X such that for any decreasing sequence {A_n : n < ω} of subsets of X with empty intersection there is a (decreasing) sequence {U_n : n < ω} of open sets with empty intersection such that A_n ⊂ U_n for all n < ω. The main motivation, apart from the set-theoretic aspects, is related to the following theorem (Kąkol--Leiderman (PAMS)): A Tychonoff space X is a ∆-space iff C_p(X) is distinguished. This result, which constitutes a significant extension of the research on distinguished spaces initiated by Dieudonne and Grothendieck on Fréchet lcs, made it possible to combine aspects of functional analysis, topology and set theory in the study of a number of objects related to the spaces C(X). We will present recently obtained new results in this topic; among others, two remarkable theorems of Juhasz--van Mill--Soukup--Szentmiklossy (2025) -- solving two important open problems in this topic. Close connections of ∆-spaces with remarkable concepts of λ-spaces and Q-spaces will be given and discussed. Let us emphasize that the latter spaces have mobilized a number of specialists both in topology and set theory. We discuss also recent results about Baire ω-resolvable spaces involving ∆-spaces. A number of open problems in this area will be provided.</p><p><br></p><p>For the Latex version of the abstract see the attached PDF on the website.</p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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