Limits of sequences of continuous functions depending on finitely many coordinates

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• 作者：Olena Karlova ; ^{maslenizza.ua@gmail.com} ; Volodymyr Mykhaylyuk ^{vmykhalyuk@ukr.net}
• 关键词：primary ; 54C30 ; secondary ; 26A21
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：216
• 期：Complete
• 页码：25-37
• 全文大小：351 K
• 卷排序：216

文摘

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.