1. A reminder of set theory

Note (application, correspondence, function, transformation and operator): The term application is competing with that of correspondence or function, although the latter often refers more specifically to applications whose starting and ending sets are sets of numbers (integers, reals, complexes). The term transformation is used to designate an application operating on functions (Fourier, wavelet, etc.) or on sets (affine, morphological, etc.). The term operator is also used in function theory and functional analysis...