19.7.2 Properties of sets

Problem: In the metric space \( (\mathbb{R} ; \rho) \) with a natural metric \( \rho(x, y)=|x-y| \) the following set is given: \( A=(-\infty ; 0) \cup[1 ; 2] \cup\{3\} \). For the set \( A \) find: 1) the interior, 2) the closure, 3) the set of limit points, 4) the set of isolated points, 5) the set of boundary points.