  We show topological genericity for the set of functions in the space X, where
X denotes the intersection of the Hardy spaces H^p with p<1, on the open unit
disc such that the sequence of Taylor coefficients of the function and of all
derivatives of the function are unbounded. Results of similar nature are valid
when the space X is replaced by H^p(0 < p < 1) and by localized versions of
such spaces. Looking at the smaller space A(D) \subseteq H^{\infty} we show
topological genericity for the set of functions in A(D) and of all derivatives
such that the sequence of Taylor coefficients of the function are outside of
(\el)^1. We also show topological genericity for the set of functions in the
space Y, where Y denotes the intersection of the harmonic Hardy spaces h^p with
p<1, whose harmonic conjugate does not belong in any h^q (q > 0)
