<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> -Polynomial Convexity and Holomorphic Convexity

We compare the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> -polynomial convexity of Guedj with holomorphic convexity away from the support of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> . In particular, we prove an Oka–Weil theorem for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> -polynomial convexity. We also show a sufficient condition for when the notions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> -polynomial convexity and holomorphic convexity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo>∖</mml:mo> <mml:mi mathvariant="normal">Supp</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> coincide in the class of complex projective algebraic manifolds.