  We establish a natural duality between the category of involutive
bisemilattices and the category of semilattice inverse systems of Stone spaces,
using Stone duality from one side and the representation of involutive
bisemilattices as P{\l}onka sum of Boolean algebras, from the other.
Furthermore, we show that the dual space of an involutive bisemilattice can be
viewed as a GR space with involution, a generalization of the spaces introduced
by Gierz and Romanowska equipped with an involution as additional operation.
