The University I go to doesn't have any courses in (classical) Algebraic Geometry so I am trying to learn myself. I am fairly comfortable with the content I have covered so far aside from a so called "easy" results which I fail to understand. So my question:
Why is the concept of a rational map between two varieties being dominant well-defined. Specifically let $X$ and $Y$ be varieties; let $U$ and $V$ be open sets of $X$; and let $(f,U)$ and $(g,V)$ be equivalent rational maps from $X$ to $Y$. Why is the image of $f$ dense in $Y$ if and only if the image of $g$ is dense in $Y$?
Thanks for any help.