Abstract
AbstractLet X be an uncountable Polish space. L̆ubica Holá showed recently that there are $$2^{\mathfrak {c}}$$
2
c
quasi-continuous real valued functions defined on the uncountable Polish space X that are not Borel measurable. Inspired by Holá’s result, we are extending it in two directions. First, we prove that if X is an uncountable Polish space and Y is any Hausdorff space with $$|Y|\ge 2$$
|
Y
|
≥
2
then the family of all non-Borel measurable quasi-continuous functions has cardinality $$\ge 2^{{\mathfrak {c}}}$$
≥
2
c
. Secondly, we show that the family of quasi-continuous non Borel functions from X to Y may contain big algebraic structures.
Publisher
Springer Science and Business Media LLC
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