 Soon after the development of the theory of rigged Hilbert spaces by Gelfand and his associates, the theory was used to develop a new formulation of quantum mechanics. This was done independently by Böhm (1966) and Roberts (1966). It was later demonstrated that the rigged Hilbert space formulation of quantum mechanics can handle a broader range of phenomena than the separable Hilbert space formulation. That broader range includes scattering resonances and decay phenomena (Böhm and Gadella 1989), as already noted. Böhm (1997) later extended this range to include a quantum mechanical characterization of the arrow of time. The Prigogine school developed an alternative characterization of the arrow of time using the rigged Hilbert space formulation of quantum mechanics (Antoniou and Prigogine 1993). Kronz (1998, 2000) used this formulation to characterize quantum chaos in open quantum systems. Castagnino and Gadella (2003) used it to characterize  decoherence  in closed quantum systems.