We prove that every continuous function $f: \mathbb{S}→ Y$, defined on the Sorgenfrey line $\mathbb{S}$, belongs to the first Baire class on $\mathbb{R}$ if $Y$ is a topological vector space. Moreover, we show for $n ≥ 1$ that every continuous function $f: \mathbb{S}^n→ Y$ belongs to the first Baire class on $\mathbb{R}^n$ if $Y$ is a metrizable arcwise connected and locally arcwise connected space.
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- ACS Style
- Karlova, O.; Fodchuk, O. Classification of continuous functions on the product of Sorgenfrey lines. Bukovinian Mathematical Journal. 2016, 3
- AMA Style
- Karlova O, Fodchuk O. Classification of continuous functions on the product of Sorgenfrey lines. Bukovinian Mathematical Journal. 2016; 3(1).
- Chicago/Turabian Style
- Olena Karlova, Olga Fodchuk. 2016. "Classification of continuous functions on the product of Sorgenfrey lines". Bukovinian Mathematical Journal. 3 no. 1.