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...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.展开更多
文摘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.
