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

Author
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.45.1.67-75
Reference
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Pages
67-75
Volume
45
Issue
1
Year
2016
Journal
Matematychni Studii
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