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...

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 ...

Abstract We show that the Cantor–Schröder–Bernstein Theorem for homotopy types, or $$\infty $$ ? -groupoids, holds in following form: For any two if each one is embedded into other, then they are equivalent. The argument developed language of type theory, Voevodsky’s univalent foundations (HoTT/UF), and requi...

in this paper we study some results on noetherian semigroups. we  show that if  $s_s$ is an  strongly  faithful $s$-act and $s$ is a duo weakly noetherian, then we have the following.

If {qn} is a lacunary sequence of integers, and if for each n, cn(x) and c-n(x) are trigonometric polynomials of degree n, then {Cn(X)} must tend to zero for almost every x whenever {cn(x)ei?nX + c-n(-x)e-i?'nX} does. We conjecture that a similar result ought to hold even when the sequence {f On} has much slower growth. However, there is a sequence of integers {nj } and trigonometric polynomial...

For each pointclass Γ ⊆ P (2) define U [Γ] as the collection of all X ⊆ 2 such that the preimage f−1(X) belongs to Γ for each continuous f : 2 → 2. We study the properties of and possible relationships among the classes U [Γ], where Γ ranges over the σ-algebras (l), (m), the completely Ramsey sets, and the sets with the Baire property. We also prove some results about cardinal coefficients of U...

Let f : C → C be a transcendental entire map that is subhyperbolic, i.e., the intersection of the Fatou set F(f) and the postsingular set P (f) is compact and the intersection of the Julia set J (f) and P (f) is finite. Assume that no asymptotic value of f belongs to J (f) and that the local degree of f at all points in J (f) is bounded by some finite constant. We prove that there is a hyperbol...

This article discusses two theorems of Georg Cantor: Cantor’s Little Theorem and Cantor’s Diagonal Theorem.These results are obtained by generalizing the method of proof ofthe well known Cantor’s theorem about the cardinalities of a setand its power set. As an application of these, Gödel’s firstincompleteness theorem is proved. Hints are given as to how to derive other deeper results including ...