$\sigma$-Sets and $\sigma$-Antisets
Ivan Gatica, Alfonso Bustamente

TL;DR
This paper explores the duality between $\sigma$-sets and $\sigma$-antisets, develops the integer space $3^{A}$ for small cardinals, and investigates algebraic properties and equations related to $\sigma$-sets.
Contribution
It introduces the $\sigma$-set-$\sigma$-antiset duality, constructs the integer space $3^{A}$ for specific cardinals, and develops properties of $\sigma$-set fusion and equations.
Findings
Established the $\sigma$-set-$\sigma$-antiset duality.
Developed the integer space $3^{A}$ for $|A|=2,3$.
Analyzed algebraic properties and equations of $\sigma$-sets.
Abstract
In this paper we present a brief study of the -set--antiset duality that occurs in -set theory and we also present the development of the integer space for the cardinals together with its algebraic properties. In this article, we also develop a presentation of some of the properties of fusion of -sets and finally we present the development and definition of a type of equations of one -set variable.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Advanced Topology and Set Theory
