%0 Journal Article
%T Partitioning of Any Infinite Set with the Aid of Non-Surjective Injective Maps and the Study of a Remarkable Semigroup
%A Charif Harrafa
%J Open Journal of Discrete Mathematics
%P 74-88
%@ 2161-7643
%D 2020
%I Scientific Research Publishing
%R 10.4236/ojdm.2020.103008
%X 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.
%K Partitioning
%K Non-Surjective
%K Injective
%K Infinite Set
%K Fixed Points
%K Lattice Structure
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=101368