On The Algebraic Structure of neutrosophic Ideal -Open Sets in Topological Spaces

Abstract

This work describes a unified study of multi-topological topological structures and neutrosophic  (neutr.) algebraic structures in accordance with the concept of the ideal to provide a new form of mathematics to accommodate uncertainty and multi-composition at once. The paper starts by generalizing open sets via the theory of -open sets and then integrates this concept with neutr. logic, that is to say, the interplay between truth, indeterminacy and falsity being its independent constituents. The integration is not a mere descriptive thing, but being explicitly formulated by expressing neutr. open sets and directly linking to a neutr. ideal in the neutr. loop, for purposes of algebraic control over the topological structure. The study offers clear, simple definitions at the fundamental level, then introduces internal concepts such as neutr. closure, inside, outside, limit, neighbor and accumulation points to illustrate the important properties in new perspective of the new framework. Most importantly, you observe the retention of the fundamental topological axioms in ideal neutr. spaces and how these are radically different from classical topology, specifically relating that to the effect of the indeterminacy complex and the function of the algebraic ideal in change of the local behavior of groups.