# Math Help - set closed but not compact

1. ## set closed but not compact

need some help with this...

Consider the set P := {(x,y) $\epsilon$ $R^2$ : $y^2 = 2x$}. Show that P is closed in $R^2$ but not compact.

Consider the set P := {(x,y) $\epsilon$ $R^2$ : $y^2 = 2x$}. Show that P is closed in $R^2$ but not compact.
$P$ is closed because the polynomial $f(x,y)=y^2-2x$ is continuous (everywhere) and $P=f^{-1}(0).$ the reason that $P$ is not compact is that it's clearly not bounded.