In this talk we will briefly introduce a general mathematical framework for group equivariance in the machine learning
context. The framework builds on a synergy between persistent homology and the theory of group actions. Our focus will be on illustrating some methods to build Goup Equivariant Non-Expansive Operators (GENEOs), which are maps between function spaces associated with groups of transformations. The development of these techniques will give us the opportunity to obtain a better approximation of thetopological space of all GENEOs.