We prove that the Kleene-Kreisel space $N^N^N$ does not satisfy Normann's
condition. A topological space $X$ is said to fulfil Normann's condition, if
every functionally closed subset of $X$ is an intersection of clopen sets. The
investigation of this property is motivated by its strong relationship to a
problem in Computable Analysis. D. Normann has proved that in order to
establish non-coincidence of the extensional hierarchy and the intensional
hierarchy of functionals over the reals it is enough to show that $N^N^N$ fails
the above condition.Comment: 10 page