Single-spin asymmetries for pions and charged kaons are measured in semi-inclusive deep-inelastic scattering of positrons and electrons off a transversely nuclear-polarized hydrogen target. The dependence of the cross section on the azimuthal angles of the target polarization ([phi]S) and the produced hadron ([phi]) is found to have a substantial sin([phi]+[phi]S) modulation for the production of [pi]+, [pi]- and K+. This Fourier component can be interpreted in terms of non-zero transversity distribution functions and non-zero favored and disfavored Collins fragmentation functions with opposite sign. For [pi]0 and K- production the amplitude of this Fourier component is consistent with zero
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