We present two important theorems in combinatorial algebraic topology and convex combinatorial geometry, these are the nerve theorem and Helly’s theorem, giving examples of their use and relevance. We show that absolute extenders are equivalent to absolute retractions and that they are topological properties which allows, for example, to obtain triangulations for topological spaces expressed in terms of the rib of the associated simplicial complex. Thus also the abstract convex structures have main relevance for metrizable spaces, in particular the convex sets are absolute extensors and therefore retracted, thus being able to obtain regular coverings and good coverings. The intersection pattern of these coverings by convex gives rise to three important combinatorial numbers, the Helly number, Radon and Caratheodory. We conclude by making evident some combinatorial properties that these...

Let p a prime number. The most familiar construction of the ring of p-adic integers ℤp, is as the projective limit of quotients of powers of the ideal (p)◁ℤ. There is another description of ℤp as a quotient of the power series ring ℤ[[X]], which can be found in some texts of p-adic analysis (see e.g. [3]). More specifically, there exists a ring isomorphism. Ψ : ℤ[[X]]/〈p − X〉 → ℤp. However, this isomorphism is also topological in nature, but there is no proof of this fact in the corresponding literature. In this article we will prove in sufficient detail that the above description is also valid in the context of topological rings.

En este artículo examinaremos algunas relaciones existentes entre los ideales principales y los conjuntos Apéry en un semigrupo numérico...

En este artículo examinaremos algunas relaciones existentes entre los ideales principales y los conjuntos Apéry en un semigrupo numérico...