Actions whose equivariant asymptotic dimension is at least two

Abstract It is proved that, for an action of a discrete group having an element of infinite order on a path‐connected compact Hausdorff space, its equivariant asymptotic dimension with respect to the family of finite subgroups is at least two. Applying this result, we show that equivariant asymptotic dimension with respect to the family of finite subgroups can be strictly greater than dynamic asymptotic dimension.