My task is this:
Show that $\partial([0,1]\times[0,1] \subset \Bbb R^2)$ is connected
My thought is that I can use the theorem that continuous image of a connected set is connected - thus I can build a continuous function that maps an interval [a,b] to $\partial([0,1]\times[0,1] \subset \Bbb R^2)$, and prove the boudary is connected. But how can such a funtion be possible and how to prove it is continuous? Also any other way to show the connectedness is welcomed. Thank you!