Induced convexity

Abstract

Everyday life sets frequently in front of us situations in which an object from a set A is replaced by another object a’ from a set B, a’ being obtained from a as its image by means of a transformation T: A → B, therefore a’ = T(a). The human perception provides us with the most known example: every object is transformed, through the senses, into a set of impulses. The synthesis of the impulses generates an “image” of that object at the level of the brain. An important problem arises in these situations: for every property p of the object a, a property p’ of the object a’ is sought for such that for each object b from A having the property p, the object T(b) has the property p\ In this case, the property p’ is said to be the image by T of the property p. The problem of the description (identification) of the property p’ is called recognition problem.