$\sigma$-Sets and $\sigma$-Antisets

In this paper we present a brief study of the $\sigma$-set-$\sigma$-antiset duality that occurs in $\sigma$-set theory and we also present the development of the integer space $3^A=⟨2^A,2^{A^{-}}⟩$ for the cardinals $\mathrm{\mid }A\mathrm{\mid }=2,3$ together with its algebraic properties. In this article, we also develop a presentation of some of the properties of fusion of $\sigma$-sets and finally we present the development and definition of a type of equations of one $\sigma$-set variable.