ABSTRACT
The theory of stability is derived from the few simple, intuitive, mechanical considerations. The extension of these relations to infinite-dimensional spaces is the motivation for the mathemathics of functional analysis, which, in a sense, enables readers to extend the simpler insights into the elastic stability of systems with finite degrees of freedom to continuous ones. In order to define the space of the configurations of the continuous elastic structural systems and to analyse their energy functionals, one necessarily have to recall those essential concepts of functional analysis. The chapter analyzes some examples of infinite-dimensional spaces that could be useful to define the configurations of continuous structural systems, for example, beams. The finite-dimensional normed spaces are simpler than the infinite-dimensional ones has many implications in the theory of stability. The rational numbers are an incomplete metric space, but if one adds the limits of all Cauchy sequences of rationals one can obtain the complete metric space of the reals.
