Partitioning of Any Infinite Set with the Aid of Non-Surjective Injective Maps and the Study of a Remarkable Semigroup

• 作者: Charif Harrafa
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Partitioning Non-Surjective INJECTIVE Infinite Set Fixed Points Lattice Structure
• 年，卷（期）: 2020,（3）
• 页码范围: 74-88
• 页数: 15页
• 分类号: O15

摘要

In this article, we will present a particularly remarkable partitioning method of any infinite set with the aid of <em>non-surjective injective</em> maps. The non-surjective injective maps from an infinite set to itself constitute a semigroup for the <em>law of composition</em> bundled with certain properties allowing us to prove the existence of remarkable elements. Not to mention a compatible equivalence relation that allows transferring the <em>said law</em> to the quotient set, which can be provided with a lattice structure. Finally, we will present the concept of <em>Co-injectivity</em> and some of its properties.