Some Properties of Primal Topologies Seen as Semirings - Garcia-Mendoza, Carlos; Vielma, Jorge; Játem, José (Topology Proceedings, 2023)
Given a set X and a function f: X → X, a topology τ_f is determined by taking the open sets to be those sets A X such that f^-1(A) A. The topological space ( X, τ_f ) is called primal space or functional Alexandroff space. In this paper, we study some properties of primal topologies seen as semirings. We prove, for example, that if ( X, τ_f ) is a connected primal space, then τ_f is a local semiring. We also determine some topological conditions for a square matrix A to be invertible, considering the primal topology τ_A generated by the matrix.