  The aim of this manuscript is to study some local properties of the
topological entropy of a free semigroup action. In order to do that we focus on
the set of entropy points of a free semigroup action, show that this set
carries the full entropy of the system (which, with respect to the chaocity of
the system, gives a fundamental relevance to such set) and obtain many
interesting properties of such set. Our results are inspired by the ones
presented in \cite{YZ}.
