Cantor-Bernstein theorem for lattice ordered groups

Cantor-bernstein Theorem for Lattices

This paper is a continuation of a previous author’s article; the result is now extended to the case when the lattice under consideration need not have the least element.

Cantor-Bernstein theorem for pseudo BCK-algebras

For any σ-complete Boolean algebras A and B, if A is isomorphic to [0, b] ⊆ B and B is isomorphic to [0, a] ⊆ A, then A B. Recently, several generalizations of this known CantorBernstein type theorem for MV-algebras, (pseudo) effect algebras and `-groups have appeared in [1], [2], [4] and [5]. We prove an analogous result for certain pseudo BCK-algebras—a noncommutative extension of BCK-algebra...

CSM25 - The Cantor-Schröder-Bernstein Theorem

Given two finite sets, questions about the existence of different types of functions between these two sets are easy to solve, as there are finitely many such functions and so one many simply enumerate them. Further more, if one has two injective functions then it is intuitively obvious that both such functions are bijections (although not necessarily the inverses of each other). However, when ...

The Hahn Embedding Theorem for Abelian Lattice-ordered Groups

A Cantor-Bernstein Theorem for Paths in Graphs

As every vertex of this graph has one “outgoing” and at most one “incoming” edge, each of those components is a cycle or an infinite path. In each of these paths and cycles we now select every other edge to mark the desired bijection. The Cantor-Bernstein problem, rephrased as above for graphs, has a natural generalization to paths. Let G be any graph, and let A and B be disjoint sets of vertic...