N^N^N does not satisfy Normann's condition
نویسنده
چکیده
We prove that the Kleene-Kreisel space 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 fails the above condition.
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