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Tuesday 19 August 2025 - 10:00 to 11:30 <br />
Place: IM, konírna
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Speaker: Jerzy Kakol, Adam Mickiewicz University in Poznań, Poland<br />
Title: Lotz-Peck-Porta and Rosenthal's theorems for spaces C_p(X)
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Abstract <br />
<p>For a Tychonoff space X by Cp(X) we denote the space C(X) of continuous real valued functions on X endowed with the pointwise topology. We show that an infinite compact space X is scattered if and only if every closed infinite-dimensional subspace in Cp(X) contains a copy of c_0 (with the pointwise topology) which is complemented in the whole space Cp(X). This provides a Cp-version of the theorem of Lotz, Peck and Porta for Banach spaces C(X) and c_0. We show also a Cp-version of Rosenthal's theorem by showing that for an infinite compact X the space Cp(X) contains a closed copy of c_{0}(\Gamma) (with the pointwise topology) for some uncountable set \Gamma if and only if X admits an uncountable family of pairwise disjoint open subsets of X.</p><p><br></p><p>The talk is based on joint research with O. Kurka and W. Śliwa.</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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