Solution
= Solution
If $p\neq q$, completeness gives a formula $\varphi$ with $\varphi\in p$ and $\neg\varphi\in q$. Then
$$
p\in[\varphi],\qquad q\in[\neg\varphi],
$$
and these two disjoint open sets cover $S_n^M(X)$. This proves the <total disconnectedness of a type space>.