Real Analysis Exchange

The Baire Classification of Strongly Separately Continuous Functions on \(\ell_\infty\)

Olena Karlova and Tomá\v{s} Visnyai

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Abstract

We prove that for any \(\alpha\in[0,\omega_1)\) there exists a strongly separately continuous function \(f:\ell_\infty\rightarrow [0,1]\) such that \(f\) belongs to Baire class \(\alpha+1\), if \(\alpha\) is finite, and Baire class \(\alpha+2\) and \(f\) does not belong to the Baire class \(\alpha\).

Article information

Source
Real Anal. Exchange, Volume 43, Number 2 (2018), 325-332.

Dates
First available in Project Euclid: 27 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.rae/1530064964

Digital Object Identifier
doi:10.14321/realanalexch.43.2.0325

Mathematical Reviews number (MathSciNet)
MR3499770

Zentralblatt MATH identifier
06924892

Subjects
Primary: 54C08: Weak and generalized continuity 54C30: Real-valued functions [See also 26-XX]
Secondary: 26B05: Continuity and differentiation questions

Keywords
strongly separately continuous function Baire classification

Citation

Karlova, Olena; Visnyai, Tomá\v{s}. The Baire Classification of Strongly Separately Continuous Functions on \(\ell_\infty\). Real Anal. Exchange 43 (2018), no. 2, 325--332. doi:10.14321/realanalexch.43.2.0325. https://projecteuclid.org/euclid.rae/1530064964


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