A Sequence of Fourier Partial Sums not Containing 2¼Q

In this paper, we focus on the bounded sequences of Fourier partial sums. Our interest is on the sequences which do not contain any rational multiple of 2¼. We construct a function on C[T] where its set of points is one of such sequences. We will show that this set is of the first category in R. Moreover the complement of this set in any arbitrary real closed interval form an uncountable set.