  We compare the $T$-polynomial convexity of Guedj with holomorphic convexity
away from the support of $T$. In particular we show an Oka--Weil theorem for
$T$-polynomial convexity, as well as present a situation when the notions of
$T$-polynomial convexity and holomorphic convexity of $X\setminus\text{Supp }T$
coincide in the context of complex projective algebraic manifolds.
