R-Compatible Ideals of topological spaces

Abstract

Abstract. This paper's goal is to present the idea of regular-compatibility of ideals by replaced the open set is Regular-open set  and with respect to topology, which is abbreviated as (τ ∼ R I ),  Using a brand-new local function termed the regular-local function A(*R) (I, T), it is also possible to examine the connection between this idea and the idea of the R-compatibility of an ideal with I. A few comparable circumstances are established. By employing the new operator is Regular -psi set short (ΨR(A)), we further analyze the characterizations of Regular -compatibility with the aid of this local function. And the relationship between  them. Several notions of compatibility between a partially ordered set and a topology on its underlying set are comparable to separation axioms and other well-known ideas from general topology.