Unbounded divergence of Fourier series of continuous functions

For any given set $E\subset[0,\,2\pi)$, of measure zero, a function $f(t)\in C(0,\,2\pi)$, is constructed whose Fourier series is unboundedly divergent on $E$. If $E$ is closed, there is a function $\varphi(t)\in C(0,2\pi)$, whose Fourier series diverges unboundedly on $E$ and converges on $[0,2\pi)\setminus E$.