Concerning the set of discontinuity of a separately continuous map (in Ukrainian) |
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| Author |
Department of Mathematics, Chernivtsi University, Kotsyubynska 2, Chernivtsi, 274000, Ukraine
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| Abstract |
One investigates the conditions on topological products $X=\prod_{s\in S}X_s$
and $Y=\prod_{t\in T}Y_t$ and topological space $Z$ for which there does not
exist a separately continuous mapping $f:X\times Y\to Z$ which set of discontinuity
consists of the only point. It is shown that if $|X_s|\ge 2$ for every $s\in S$,
$|S|>\tau$ for a cardinal $\tau$, $x_0,y_0)\in X\times Y$,
$\xi(x_0(s),X_s)\le\tau$ for every $s\in S$ and $Z$ is a regular space with
$\xi(Z)\le\tau$ then there does not exist a separately continuous mapping
$f:X\times Y\to Z$ with set of discontinuity is equal to $\{(x_0,y_0)\}$.
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| Keywords |
topological product, separately continuous mapping, set of discontinuity
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| DOI |
doi:10.30970/ms.3.1.91-94
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Reference |
1. Namioka J. Separate continuity and joint continuity // Pacif. J. Math. 1974. V.51, No 2. P. 515–531.
2. Piotrowski Z. Separate and joint continuity // Real Anal. Exch. 1985-86. V.11, No 2. P.293–322. 3. Михайлюк В.В. Про нарiзно неперервнi фунцiї на добутках тихоновських кубiв. – Чернiвцi, 1991 – 8с. – Деп. в УкрНДIНТI, N1638–Ук91. 4. Маслюченко В.К., Михайлюк В.В., Собчук О.В. Оберненi задачi теорiї нарiзно неперервних вiдображень // Укр. мат. журн. 1992. Т.44, № 9. C.1209–1220. 5. Энгелькинг Р. Общая топология. – М:Мир, 1986. – 751с. Department of Mathematics, Chernivtsi University, Kotsyubynska 2, Chernivtsi, 274000, Ukraine |
| Pages |
91-94
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| Volume |
3
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| Issue |
1
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| Year |
1994
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |