Is A open or closed? Is it a bounded set? Verify if the given set $A$ it's open or closed. Also verify if it's bounded.
a) $A = \{ (x,y) \in \mathbb{R}^2 \mid x^2 + y^2 < 1\}$
I just want the method for verify this things in case of this example, because I have items a,b,c,d,e to do. The other sets are usually points of $\mathbb{R}^2$.

Some highlights: suppose $\;\{(x_n,y_n)\}\subset \Bbb R^2\setminus A\;$ convergent, then we have that
$$\begin{cases}x_n\xrightarrow[n\to\infty]{}x_0\\{}\\y_n\xrightarrow[n\to\infty]{}y_0\end{cases}\;\;\;\text{and}\;\;(x_0,y_0)\in\Bbb R^2\setminus A$$
as we know from limits in the real line, and thus the complement of $\;A\;$ is closed so $\;A\;$ is open. It also is trivially bounded, say by the unit circle.
