Kontinuitätssatz

Theorem.

$G\subset {ℂ}^n$ is pseudoconvex if and only iffor any family of closed analytic discs ${\mathrm{\{}{d}_{\alpha }\mathrm{\}}}_{\alpha \mathrm{\in }I}$in $G$ with ${\mathrm{\cup }}_{\alpha \mathrm{\in }I}\mathrm{\partial }\mathit{}{d}_{\alpha }$ beinga relatively compact set in $G$then ${\mathrm{\cup }}_{\alpha \mathrm{\in }I}{d}_{\alpha }$ is alsoa relatively compact set in $G$.

This is the analogue of one of the definitions of a convex set. Just replacepseudoconvex with convex and closed analytic discs with closed line segments.