On topologies defined by neighbourhood operators of approximation spaces

Abstract

We consider properties of an approximation space with a neighbourhood operator. Two types of topologies τ and σ are introduced on the approximation space using a neighbourhood operator and we show that they are the same Alexandrov topology, τ=σ. Also, for a reflexive and transitive neighbourhood operator, the topological space (U,σ) is a Hausdorff space if and only if σ is the discrete topology P(U), where U is a non-empty set which is not need to be finite. In addition, we prove an algebraic property that a pair (n,apr_) of operators defined by a neighbourhood operator n forms a Galois connection.