## Real Analysis Exchange

- Real Anal. Exchange
- Volume 40, Number 2 (2015), 371-382.

### On Baire Classification of Strongly Separately Continuous Functions

#### 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 $G$.

#### Article information

**Source**

Real Anal. Exchange, Volume 40, Number 2 (2015), 371-382.

**Dates**

First available in Project Euclid: 4 April 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.rae/1491271222

**Mathematical Reviews number (MathSciNet)**

MR3499770

**Zentralblatt MATH identifier**

06848841

**Subjects**

Primary: 54C08: Weak and generalized continuity 54C30: Real-valued functions [See also 26-XX]

Secondary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]

**Keywords**

strongly separately continuous function Baire classification

#### Citation

Karlova, Olena. On Baire Classification of Strongly Separately Continuous Functions. Real Anal. Exchange 40 (2015), no. 2, 371--382. https://projecteuclid.org/euclid.rae/1491271222