Some Generic Results in Mathematical Physics
2004, v.10, №3, 517-521
We discuss three consequences of the Baire Category Theorem. In spaces of long-range interactions, typical phase diagrams are trivial. Most ergodic states of a lattice system are not Gibbs states. Unitarily-equivalent self-adjoint operators on Hilbert space with purely discrete spectrum usually can't be added.
Keywords: generic sets,very sparse sets,generic nonGibbsianness,generic lack of self-adjointness properties