Maps from the 1.3 mm observations of the B335 core. Top left: total intensity (Stokes I) thermal dustemission in color scale. The emission is shown from 3σ_I where σ_I is the rms noise in the Stokes I map. Top right: polarized intensity P in colorscale.Bottom left: polarization fraction in colorscale,shown where I > 3σ_I. Bottom right: dispersion of polarization position angles in color scale; the pixel size corresponds to the pixel size considered in the statistics. The dashed white contour represents the 5σ_I level. The solid white contour represents the threshold level of Stokes I calculated as described in Sect. 3.1, above which the mean S/N of P > 5. The beam size is 1.′′14 × 0.′′ 90, with a position angle of 89.1°.