Continuity of inversion in a Banach algebra
= Continuity of inversion in a Banach algebra
{title2=$a\mapsto a^{-1}$}
Inversion is continuous on the <group of invertible elements of a Banach algebra>. The <Neumann series> gives a local bound on inverse norms, while $b^{-1}-a^{-1}=b^{-1}(a-b)a^{-1}$ makes the difference tend to zero as $b\to a$.