Algunos aspectos de la teoría de (ultra)filtros

Abstract

The notions of filter and ultrafilter are introduced in the field of General Topology to extend the notion of convergence sequences. Specifically, a filter F on a set X is a nonempty family of subsets of X such that F does not contain the empty set, for any two elements of F their intersection is also in F and every superset of every element of F is also an element of F. The family of filters on a set admits a partial ordering for which one can obtain at least one maximal element called ultrafilter on X. In this paper we will study the usual fundamental properties of these objects within Set Theory and General Topology as well as some examples of applications to other mathematical areas such as Combinatorics, Graph Theory and NonStandard Analysis.