TITLE:
Partitioning of Any Infinite Set with the Aid of Non-Surjective Injective Maps and the Study of a Remarkable Semigroup
AUTHORS:
Charif Harrafa
KEYWORDS:
Partitioning, Non-Surjective, Injective, Infinite Set, Fixed Points, Lattice Structure
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.10 No.3,
July
9,
2020
ABSTRACT: In this article, we will present a particularly remarkable partitioning method of any infinite set with the aid of non-surjective injective maps. The non-surjective injective maps from an infinite set to itself constitute a semigroup for the law of composition bundled with certain properties allowing us to prove the existence of remarkable elements. Not to mention a compatible equivalence relation that allows transferring the said law to the quotient set, which can be provided with a lattice structure. Finally, we will present the concept of Co-injectivity and some of its properties.