Abstract
Some concepts of convergence used in mathematical chemistry are briefly reviewed: number convergence, uniform and non-uniform function convergence, convergence in norm and binary product, operator convergence, computer convergence, etc. Some properties of the abstract Hilbert space and some of its realizations in mathematical chemistry are discussed. Finally, it is pointed out that the scattering wave functions of importance in the theory of chemical reactions are limit points of theL2Hilbert space — not in the norm, but in the sense of a non-uniform point-by-point convergence, which is of essential value in practical applications.
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