Certain approximation spaces using local functions via idealization

Abstract

In this paper, we use the notion of upper set R(A) to define the local function and closure operator cl * R (A) in an ideal approximation space (X, R, L ). This, ideal approximation space (X, R, L ) based on an ideal L joined to the approximation space (X, R) are introduces as well. The approximation axioms T i , i = 0, 1, 2 are introduced in the approximation space and also in the ideal approximation spaces. Examples are given to explain the definitions . Connectedness in approximation spaces and ideal connectedness are introduced and the differences between them are explained.