Strongly separately continuous functions and a characterization of open sets in a box-product (in Ukrainian) |
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| Author |
Maslenizza.ua@gmail.com
Yuriy Fedkovych Chernivtsi National University
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| 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 $W=f^{-1}((0,1])$.
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| Keywords |
strongly separately continuous function; small box-product; almost open set
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| DOI |
doi:10.15330/ms.43.1.36-42
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| 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 (1998-99), 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 |
36-42
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| Volume |
43
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| Issue |
1
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| Year |
2015
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| Journal |
Matematychni Studii
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