  We investigate wether three statements in analysis, that can be proved
classically, are realizable in the realizability model of extensional
continuous functionals induced by Kleene's second model $K_2$. We prove that a
formulation of the Riemann Permutation Theorem as well as the statement that
all partially Cauchy sequences are Cauchy cannot be realized in this model,
while the statement that the product of two anti-Specker spaces is anti-Specker
can be realized.
