A Topological Space Defined on Finite Rings Modulo Composite Number

For a composite number 𝒏, we explore a topological space on the ring of integers modulo 𝒏, we usebasis sets formed by solutions to quadratic residue equations,where elements are unitsmodulo 𝒏. This definitionallows us to investigate the algebraic relationships among solutions, focusing on properties like clopen sets, closure, and interior operations. Additionally, we examine the continuity of mappings between the group of units in ℤ/𝒏ℤand quadratic residues, alongside the quotient topology induced on this group of units. Acomparison of the separation properties of these topological spaces is also presented.