  Group equivariant operators are playing a more and more relevant role in
machine learning and topological data analysis. In this paper we present some
new results concerning the construction of $G$-equivariant non-expansive
operators (GENEOs) from a space $\varPhi$ of real-valued bounded continuous
functions on a topological space $X$ to $\varPhi$ itself. The space $\varPhi$
represents our set of data, while $G$ is a subgroup of the group of all
self-homeomorphisms of $X$, representing the invariance we are interested in.
