Contractibility of $\mathbb{R}^2$ when we remove the $x$-axis

Question

Question: Is $\mathbb{R}^2$ minus the $x$-axis contractible?

I'm doing differential equation and I have to decide if the domain is contractible, and I'm wondering if the above domain is.

Is it contractible because it is the real line?

Answer 1

Every contractible space is connected.

$\qquad$A contractible space is path connected.

But if you remove a line from $\mathbb{R}^2$, the resulting space is not connected.