El espacio de Golomb y su no conexidad en pequeño

Abstract

In the present paper we study Brown spaces which are connected and not completely Hausdorff.Using arithmetic progressions, we construct a base B G for a topology τ G on N, and show that (N, τ G ), called the Golomb space is a Brown space.We also show that some elements of B G are Brown spaces, while others are totally separated.We write some consequences of such result.For example, the space (N, τ G ) is not connected "im kleinen" at each of its points.This generalizes a result proved by Kirch in 1969.We also present a simpler proof of a result given by Szczuka in 2010.

Locations

• Revista Integración - View - PDF
• Dialnet (Universidad de la Rioja) - View - PDF
• LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) - View - PDF