The aim of this paper is to study Iseki spaces of distinguished classes of ideals of a semiring endowed with a topology. We show that every Is\'{ e}ki space is quasi-compact whenever the semiring is Noetherian. We characterize Is\'{ e}ki spaces for which every non-empty irreducible closed subset has a unique generic point. Furthermore, we provide a sufficient condition for the connectedness of Is\'{ e}ki spaces and show that the strongly connectedness of an Is\'{ e}ki space implies the existence of non-trivial idempotent elements of semirings.
Categories: math.RA