The investigation of the nuclei of galaxies and quasars has been central to modern astronomy. The application of the technique of very-long-baseline interferometry (VLBI) to such sources has allowed the mapping of their angular radio brightness distributions and the analysing of their temporal changes. Many radio galaxies and quasars consist of a compact core, or centre of activity, and collimated jets of material ejected from the core with relativistic velocities1. Of particular interest are the brightness distributions and kinematics of the cores of such sources, because they may contain a supermassive object (SMO), possibly a black hole2 (but see ref. 3 for an alternative view), with a mass of ∼109 M ⊙(ref. 4) and a Schwarzschild radius of ∼3 x l014cm. We present here global VLBI observations of 11 radio sources at a wavelength of 7 mm, including a map of the brightness distribution of the active galactic nucleus in 3C84. This map has an angular resolution of 100 microarcseconds, unsurpassed in an image of a celestial object.