A high-resolution recoil-ion momentum spectrometer based on a precooled localized supersonic jet target (COLTRIMS) has been combined with a novel low-energy electron analyzer with 4 pi solid angle for electrons with energies E(e) less than or similar to 30 eV including E(e) = 0 eV. Thus, three recoil-ion momentum components, the recoil-ion charge state and three momentum components of one electron emitted in any collision-induced ionization reaction are measured simultaneously with a coincidence efficiency of 28%. In order to accept large recoil-ion longitudinal momenta (along the beam) of p(R parallel to) less than or equal to 160 a.u. and simultaneously guarantee a superior resolution in this direction (Delta P-R parallel to less than or equal to +/-0.08 a.u.), recoil ions are extracted in the longitudinal direction different from all former concepts. Test measurements, details on the present design and results of a kinematically complete experiment for single ionization are presented and possible further improvements are discussed. The future potential of such spectrometers for the investigation of collision-induced atomic many-particle reactions, the ''Coulomb-explosion'' of molecules and the spectroscopy of electronic states in heavy few-electron systems is illustrated. Similar techniques might be used to measure angular correlations and even the neutrino mass in P-decay experiments.