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

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