Let $X$ be a irreducible complex projective variety. Consider a rational map of complex projective varieties $f\colon X\longrightarrow Y$, i.e. a morphism $U\longrightarrow Y$, where $U$ is a Zariski-open of $X$. In the analytic topology the morphism $U^{an}\longrightarrow Y^{an}$ is continuos and moreover, it's very well known that $U^{an}$ is dense in $X^{an}$, as $U$ is dense in $Y$.
My question is:
Is it possible extend the map $U^{an}\longrightarrow Y^{an}$ to a continuos map $X^{an}\longrightarrow Y^{an}$?