The axiomatization given by von Neumann lasted for more than half a century in most of the classical books of quantum mechanics. However, in the 1990's the majority of physicists began to adopt a critical attitude towards this form of postulation, especially regarding the intuitive development and the treatment of the problem of collapse of the wave function. It should be noted that the experimental conclusions reached with any set of axioms that can be chosen are, and in fact must be, exactly the same. In fact for most physicists, who do not work on the foundations of quantum mechanics, this is a transparent question. The concept of rigged space is related to topological characteristics that link the square-integrable aspects to those of distribution in functional analysis. This allows us to include a series of generalized functions due to Dirac.