On strongly separately continuous functions on sequence spaces

2015/12/06 by Olena Karlova, Karlova, Olena, Tomáš Visnyai +1
Mathematics · #26B05 #54C08 #54C30 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:26B05 #msc:54C08 #msc:54C30

paper · pdf · doi:10.48550/arxiv.1512.01757

arxiv created 2015/12/06 · arxiv updated 2015/12/08

Abstract

We study strongly separately continuous real-valued function defined on the Banach spaces ℓ_p. Determining sets for the class of strongly separately continuous functions on ℓ_p are characterized. We prove that for every 1≤ α<ω₁ there exists a strongly separately continuous function which belongs the (α+1)'th Baire class and does not belong to the α'th Baire class on ℓ_p. We show that any open set in ℓ_p is the set of discontinuities of a strongly separately continuous real-valued function.

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