  We introduce and develop a topological semantics of conservativity logics and
interpretability logics. We prove the topological compactness theorem of
consistent normal extensions of the conservativity logic $\mathbf{CL}$ by
extending Shehtman's ultrabouquet construction method to our framework. As a
consequence, we prove that several extensions of $\mathbf{CL}$ such as
$\mathbf{IL}$, $\mathbf{ILM}$, $\mathbf{ILP}$ and $\mathbf{ILW}$ are strongly
complete with respect to our topological semantics.
