On strict homological dimensions of algebras of continuous functions

We prove that, for each nonnegative integer $n$ and $n=\infty$, there exists a compact topological space $\Omega$ such that the strict global dimension and the strict bidimension of the Banach algebra $C(\Omega)$ of all continuous functions on $\Omega$ are equal to $n$. We also obtain several “additivity formulas” for the strict homological dimensions of strict Banach algebras.