D∗-Local Functions in Ideal Spaces

Abstract

In this study, a novel operation is introduced, which creates a local function of A regard to I and τ respectively denoted as A_D∗(I,τ)={y∈Y|V∩A∉I, for each V∈τ^D(y)} where τ^D(y)={V∈τ^D|y∈V}. We then look into some of the fundamental characteristics and attributes of A_D∗(I,τ). Additionally, we look into an operator η: P(Y)→τ provides η(E)=Y−[Y−E]_D∗ for all E∈P(Y). Then the closure operator cl_D∗(E)=E_D∗∪E which forms the topology and the relation τ_D∗={V⊆Y|cl_D∗(Y−V)=Y−V}.