I found in "Several complex variables" by Jaap Korevaar and Jan Wiegnerick (https://www.math.stonybrook.edu/~ebedford/PapersForM537/WiegerinckKorevaar.pdf) in Chapter 1.2 that the boundary of a bidisc centered at $a = (0,0) = 0$ is defined as the disjoint union $$ \{ C(0,r_1) \times \Delta(0,r_2) \} \ \cup \ \{ \Delta(0,r_1) \times C(0,r_2) \} \ \cup \ \{ C(0,r_1) \times C(0,r_2) \} $$,
where $\Delta(0,r_j) = \{z \in \mathbb C^2 : |z_j| < r_j, \ j=1,2\} $ are the discs and $C(0,r_j) = \{z \in \mathbb C^2 : |z_j| = r_j, \ j=1,2\} $ are the circles. The bidisc with polyradius $r = (r_1, r_2)$ is then $\Delta(0,r) = \Delta(0,r_1) \times \Delta(0,r_2)$.
My first question is: Why do we need for the boundary the parts $\{ C(0,r_1) \times \Delta(0,r_2) \}$ and $\{ \Delta(0,r_1) \times C(0,r_2) \}$ ? Why isn't $\{ C(0,r_1) \times C(0,r_2) \}$ enough for the boundary? Since in 1D complex space (2D real space), the boundary of a disc is precisely the circle "around" it.
Second question: What exactly is it meant with the disjoint union? From the definition of a disjoint union, for example from Wikipedia (https://en.wikipedia.org/wiki/Disjoint_union) it has to do something with indexing from which set the value comes (as far as I understand)