Strongly separately continuous functions and a characterization of open sets in a box-product (in Ukrainian)

Author
O. Karlova
Yuriy Fedkovych Chernivtsi National University
Abstract
We prove that a subset $W$ is open in a small box-product $\mathop{\boxdot}_{n\in\mathbb N} X_n$ 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 box-product; almost open set
DOI
doi:10.15330/ms.43.1.36-42
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), 1118.

2. O. Dzagnidze, Separately continuous function in a new sense are continuous, Real Anal. Exchange, 24 (1998-99), 695702.

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), 2, 499510.

Pages
36-42
Volume
43
Issue
1
Year
2015
Journal
Matematychni Studii
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