In this paper we prove that the extended spectrum Σ (x), defined by W. Żelazko, of an element x of a pseudo-complete locally convex unital complex algebra A is a subset of the spectrum σA(x), defined by G.R. Allan.Furthermore, we prove that they coincide when Σ(x) is closed.We also establish some order relations between several topological radii of x, among which are the topological spectral radius Rt(x) and the topological radius of boundedness βt(x).