Partitioning of Any Infinite Set with the Aid of Non-Surjective Injective Maps and the Study of a Remarkable Semigroup
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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.
Keywords:
Partitioning,
Non-Surjective,
Injective,
Infinite Set,
Fixed Points,
Lattice Structure
Cite this paper:
Harrafa, C. (2020) Partitioning of Any Infinite Set with the Aid of Non-Surjective Injective Maps and the Study of a Remarkable Semigroup. Open Journal of Discrete Mathematics, 10, 74-88. doi: 10.4236/ojdm.2020.103008.
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