Stability and equivariant Gromov--Hausdorff convergence

We give applications of equivariant Gromov–Hausdorff convergence in various contexts. Namely, using equivariant Gromov–Hausdorff convergence, we prove a stability result in the setting of compact finite dimensional Alexandrov spaces. Moreover, we introduce the notion of an \emph{almost commutative diagram} and show that its use simplifies both exposition and argument.