  We prove that if a function $f$ is continuous in an open subset
$U\subset\mathbb{C}$ and analytic in $U\setminus X$, where $X\subset U$ is a
Polish space having characteristic system $(i,n)$, such that $i\in\{0,1\}$ and
$n\in\mathbb{N}$, then the complex integral line of $f$ along the boundary of
any triangle in $U$ vanishes.
