Open and connected set

Question

Show that $D:=\{{(x,y)\in R^2 : y>1,x<4,y<\sqrt{x}}\}$ is an open set. Show that D is a connected set. my attempt was to use interior points but since is in $R^2$ I get confused. thanks for your help

Answer 1

It happens that your set isn't open. For instance, $(1,2)\in D$, but no point of the form $\left(1,2-\frac1n\right)$ (with $n\in\mathbb N$) is an element of $D$.

Answer 2

If you sketch the set you'll be able to show by inspection if it is path connected and thus connected. Regarding closure, a quick glance at the inequalities would indicate that it isn't open.