To let $ pi: mathbb {R} ^ {2} to mathbb {R} $ be the projection of $ pi (x, y) = x $,

Is there a simple curve with a closed plane? $ gamma: I to mathbb {R} ^ {2} $ so for all $ t in I $, we have $ pi ( gamma & # 39; t) ge 0 $?

I tried to define the reparmization of $ gamma $ such as $ tilde { gamma} $ and tried to use Hopf's circulation set, but could not do it. Can you help?