Published online by Cambridge University Press: 09 April 2009
Let (X, T, π) be a topological transformation group, where X is a Hausedorff continuum. We will say that X is irreducibly T-invariant if no proper subcontinuum of X is T-invariant. Wallace, [6], has shown that if T is abelian and X is irreducibly T-invariant, then X has no cut point; he then asked if this statement remains true if “abelian” is replaced by “compact”. In this paper we answer this question in the affirmative, and prove a related result when T satisfies a recursive property.