Limits of sequences of continuous functions depending on finitely many coordinates
General Topology
2016-03-03 v1
Abstract
We answer two questions from {\it V.Bykov, On Baire class one functions on a product space, Topol. Appl. {199} (2016) 55--62,} 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.
Keywords
Cite
@article{arxiv.1603.00650,
title = {Limits of sequences of continuous functions depending on finitely many coordinates},
author = {Olena Karlova and Volodymyr Mykhaylyuk},
journal= {arXiv preprint arXiv:1603.00650},
year = {2016}
}