In this paper, we study some structure spaces of (m,n)-semiring (S, f , 1), introducing the classes of n-ary prime k-ideals, n-ary prime full k-ideals, n-ary prime ideals, maximal ideals and strongly irreducible ideals. Considering their collections, respectively, of an (m,n)-semiring (S, f , 1), we construct the respective topologies on them by means of closure operator defined in terms of intersection and inclusion relation among these ideals of the (m,n)-semiring (S, f , 1). The obtained topological spaces are called the structure spaces of (m,n)-semiring (S, f , 1). We mainly study several principal topological axioms and properties of those structure spaces of (m,n)-semiring such as separation axioms, compactness and connectedness etc.