Resumen de El orden de especialización en estructuras débiles generalizadas

Jesús Ávila, Adriana Grajales, Leidy Carolina Perdomo Hernández

• español

  En este trabajo desarrollamos una teoría del orden de especialización en estructuras débiles generalizadas. Relacionamos varios conceptos topológicos con conceptos de conjuntos ordenados y estudiamos el conjunto de estructuras sobre el conjunto cuyo orden de especialización coincide con un orden inicial . Finalmente probamos que este conjunto tiene como elemento máximo a la topología de Alexandroff , pero en general no tiene elemento mínimo.

• English

  In topology it is well-known that it is possible to move from topology to partial ordered sets and vice versa, using the specialization order and Alexandrov’s topology among others.

  This relationship has allowed to obtain important theoretical results, which have been generalized when considering preorder relations or better yet binary relations. Following the classical methodology of mathematical works, that is, using theorems, propositions, corollaries, examples and counterexamples, in this work we develop a theory of the specialization order in generalized weak structures. We relate several topological concepts with ordered set concepts and study the set of ?? structures on the set ? whose specialization order coincides with an initial order ≤.

  Finally we prove that this set has as a maximum element Alexandroff’s topology, but in general it does not have a minimum element.