  Let $G$ be a bounded simply connected domain in the complex plane. A point
$a\in \partial G$ is said to be accessible from inside of $G$ if there is a
Jordan arc $J$ such that $J\subset \bar G$ and $J\cap\partial G=\{a\}$. In this
paper the author shows that a univalent analytic function $\psi$ from the unit
disk $D$ onto $G$ extends continuously to $\bar D$ if and only if every
$a\in\partial G$ is accessible. The main result covers a famous theorem proved
by C. Carathe\"{o}dory, which says that if $G$ is a Jordan domain, then $\psi$
extends to be a homeomorphism from $\bar D$ onto to $\bar G$.
