Discontinuity points of separately continuous mappings with values in the Sorgenfrey line (in Ukrainian) 

Author 
vmaslyuchenko@ukr.net, myronyk.oks@gmail.com
Chernivtsi National University

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 $A\times \{b\}$.

Keywords 
Sorgenfrey line; separately continuous mapping

DOI 
doi:10.15330/ms.45.1.6775

Reference 
1. Filipchuk O.I. Separately continuous mappings and their analogues with values in nonmetrizable 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 KCfunctions// Int. Conf. dedicate to the 125th anniversary of Hans Hahn. Book of Abstracts.  2004.  P. 6566. (in Ukrainian) 4. Maslyuchenko V.K., Myronyk O.D. The Sorgenfrey line and separately continuous mappings, Buk. Math. J.  2014.  V.2, ¹1.  P. 5968. (in Ukrainian) 5. Breckenridge J.C., Nishiura T. Partial continuity, quasicontinuity and Baire spaces// Bull. Inst. Acad. Sinica.  1976.  V.4, ¹2.  P. 191203. 6. Calbrix J., Troallic J.P. Applications separement continues// C.R. Acad. Sc. Paris. Sec. A.  1979.  V.288.  P. 647648. 
Pages 
6775

Volume 
45

Issue 
1

Year 
2016

Journal 
Matematychni Studii

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