Characterization and uniqueness of $\sigma$-Antisets

TL;DR

This paper proves the uniqueness of $\sigma$-antisets for $\sigma$-sets and provides a characterization of such antisets, advancing the theoretical understanding of these mathematical structures.

Contribution

It establishes the uniqueness of $\sigma$-antisets and offers a characterization, which was not previously known in the theory of $\sigma$-sets.

Findings

Uniqueness of $\sigma$-antisets proven

Characterization of $\sigma$-antisets provided

Theoretical advancement in $\sigma$-set theory

Abstract

In this article, we prove that if there exists a $\sigma$-antiset $X^{*}$, of a $\sigma$-set $X$, then it is unique and therefore we can present a characterization of the $\sigma$-antiset.