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 AD∗(I,τ)={y∈Y|V∩A∉I, for each V∈τD(y)} where τD(y)={V∈τD|y∈V}. We then look into some of the fundamental characteristics and attributes of AD∗(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 clD∗(E)=ED∗∪E which forms the topology and the relation τD∗={V⊆Y|clD∗(Y−V)=Y−V}.