Discontinuity points of separately continuous mappings with values in the Sorgenfrey line (in Ukrainian) |
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| Author |
vmaslyuchenko@ukr.net, myronyk.oks@gmail.com
Chernivtsi National University
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| Abstract |
We prove the following results. Let $X$ and $Y$ be topological
spaces with $Y$ first countable. If $f\colon X\times Y\to \mathbb L$ is a
separately continuous mapping with values in the Sorgenfrey line $\mathbb L$ then for every $y\in Y$ the set $D_y(f)=\{x\in X\colon (x,y)$
is a discontinuity point of $f$
is meager in $X$. Conversely, for every meager $F_\sigma$-set $A$ in $\mathbb L$ and for arbitrary point $b$
of the rational line $\mathbb Q$ we construct the separately continuous mapping $f\colon \mathbb L\times\mathbb Q\to \mathbb L$, such that
the set of all discontinuity points is equal to $A\times \{b\}$.
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| Keywords |
Sorgenfrey line; separately continuous mapping
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| DOI |
doi:10.15330/ms.45.1.67-75
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| Reference |
1. Filipchuk O.I. Separately continuous mappings and their analogues with values in non-metrizable spaces.
- PhD thesis, 2010. (in Ukrainian)
2. Myronyk O.D. Stratifiable, semistratifiable spaces and separately continuous mappings. - PhD thesis, 2015. (in Ukrainian) 3. Maslyuchenko V.K., Filipchuk O.I. The importance of the $\sigma$-metrizability in results on joint continuity of KC-functions// Int. Conf. dedicate to the 125th anniversary of Hans Hahn. Book of Abstracts. - 2004. - P. 65-66. (in Ukrainian) 4. Maslyuchenko V.K., Myronyk O.D. The Sorgenfrey line and separately continuous mappings, Buk. Math. J. - 2014. - V.2, ¹1. - P. 59-68. (in Ukrainian) 5. Breckenridge J.C., Nishiura T. Partial continuity, quasicontinuity and Baire spaces// Bull. Inst. Acad. Sinica. - 1976. - V.4, ¹2. - P. 191-203. 6. Calbrix J., Troallic J.P. Applications separement continues// C.R. Acad. Sc. Paris. Sec. A. - 1979. - V.288. - P. 647-648. |
| Pages |
67-75
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| Volume |
45
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| Issue |
1
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| Year |
2016
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |