Strongly separately continuous functions and a characterization of open sets in a boxproduct (in Ukrainian) 

Author 
Maslenizza.ua@gmail.com
Yuriy Fedkovych Chernivtsi National University

Abstract 
We prove that a subset $W$ is open in a small boxproduct $\mathop{\boxdot}_{n\in\mathbb N} X_n$ of a sequence of pointed spaces, every finite product of which is a perfect paracompact Hausdorff space, if and only if there exists a strongly separately continuous function $f$ with values in $[0,1]$ and defined on a $\sigma$product of the sequence $(X_n)_{n=1}^\infty$ equipped with the Tychonoff topology such that $W=f^{1}((0,1])$.

Keywords 
strongly separately continuous function; small boxproduct; almost open set

DOI 
doi:10.15330/ms.43.1.3642

Reference 
1. J. Cincura, T. Salat, T. Visnyai, On separately continuous functions $f\colon \ell^2\to\mathbb R$, Acta Acad. Paedagog.
Agriensis, XXXI (2004), 11–18.
2. O. Dzagnidze, Separately continuous function in a new sense are continuous, Real Anal. Exchange, 24 (199899), 695–702. 3. O. Karlova, On Baire classification of strongly separately continuous functions, Real Anal. Exch. (accepted). 4. O. Karlova, V. Mykhaylyuk, On strongly separately continuous mappings on products, Math. Slovaca (accepted). 5. T. Visnyai, Strongly separately continuous and separately quasicontinuous functions $f\colon \ell^2\to\mathbb R$, Real Anal. Exchange, 38 (2013), ¹2, 499–510. 
Pages 
3642

Volume 
43

Issue 
1

Year 
2015

Journal 
Matematychni Studii

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