Limits of sequences of continuous functions depending on finitely many coordinates

作者：Karlova Olena^*; Mykhaylyuk Volodymyr

来源：Topology and Its Applications, 2017, 216: 25-37.

DOI：10.1016/j.topol.2016.11.013

• Baire class one
• Dependence of finitely many coordinates
• Semicontinuous function

We answer two questions from Bykov (2016) [2] and prove that every Baire one function on a subspace of a countable perfectly normal product is the pointwise limit of a sequence of continuous functions, each depending on finitely many coordinates. It is proved also that a lower semicontinuous function on a subspace of a countable perfectly normal product is the pointwise limit of an increasing sequence of continuous functions, each depending on finitely many coordinates, if and only if the function has a minorant which depends on finitely many coordinates.

• 出版日期2017-2-1