Is the set $\{x \in \mathbb{R}^3 : |x_1-2| + |x_2-1| \leq 2\}$ is compact?
I know that if $x \in \mathbb{R^2}$, then the previous set would be compact. However, there is an extension, and the topology is a bit different.
Is anyone could comment this set?
Hint: Let $C \subset \mathbb R^2$ be the set of $x = (x_1, x_2)$ that satisfy $|x_1-2| + |x_2-1| \leq 2$. Then your set is $C \times \mathbb R$. Does that look compact under the usual topology?