Semadeni-Pełczyński derivative and Banach spaces of continuous functions on nonmetrizable cubes

Speaker(s)

Maciej Korpalski

Affiliation

University of Wrocław

Language of the talk

Polish

Date

April 29, 2026, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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We study Banach spaces C(K) of real-valued continuous functions on finite products of compact lines. It turns out that the topological character of these compact lines can be used to distinguish whether two spaces of continuous functions on products are isomorphic or embeddable to each other. Especially, if K_1, ..., K_n, L_1, ..., L_k are compact lines of uncountable character and k and n are different, then the spaces C(K_1 x K_2 x ... x K_n) and C(L_1 x L_2 x ... x L_k) are not isomorphic.
The results are obtained by developing methods used by Semadeni in 1960 and Candido in 2022.
The talk is based on the preprint: https://arxiv.org/abs/2502.16981

 

 

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