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2015 On Baire Classification of Strongly Separately Continuous Functions
Olena Karlova
Real Anal. Exchange 40(2): 371-382 (2015).

Abstract

We investigate strongly separately continuous functions on a product of topological spaces and prove that if $X$ is a countable product of real lines, then there exists a strongly separately continuous function $f:X\to\mathbb{R}$ which is not Baire measurable. We show that if $X$ is a product of normed spaces $X_n$, $a\in X$ and $\sigma(a)=\{x\in X:|\{n\in\mathbb{N}: x_n\ne a_n\}|\lt\aleph_0\}$ is a subspace of $X$ equipped with the Tychonoff topology, then for any open set $G\subseteq \sigma(a)$, there is a strongly separately continuous function $f:\sigma(a)\to \mathbb{R}$ such that the discontinuity point set of $f$ is equal to $G$.

Citation

Download Citation

Olena Karlova. "On Baire Classification of Strongly Separately Continuous Functions." Real Anal. Exchange 40 (2) 371 - 382, 2015.

Information

Published: 2015
First available in Project Euclid: 4 April 2017

zbMATH: 06848841
MathSciNet: MR3499770

Subjects:
Primary: 54C08, ‎54C30
Secondary: 26A21

Rights: Copyright © 2015 Michigan State University Press

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Vol.40 • No. 2 • 2015
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