Remark

Suppose that $X$ has only ajinite number of distinct irreducible components $X_i$ ($1 \leq i \leq n$); then $U_+ = \mathbf{C}(\bigcup_{j \neq i} X_j)$ is open in $X$ and dense in $X_i$ since $X_i \notin \bigcup_{j \neq i} X_j$; the $U_i$ ($1 \leq i \leq n$) are therefore non-empty open sets of $X$ which are irreducible (Proposition 2), pairwise disjoint and with their union dense in $X$.