International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 51, Pages 3217-3239
doi:10.1155/S0161171203212230

An extension theorem for sober spaces and the Goldman topology

Ezzeddine Bouacida,1 Othman Echi,2 Gabriel Picavet,3 and Ezzeddine Salhi1

 1Département de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, BP 802, Sfax 3018, Tunisia
2Department of Mathematics, Faculty of Sciences of Tunis, University Tunis-El Manar, “Campus Universitaire”, Tunis 1092, Tunisia
3Laboratoire de Mathématiques Pures, Université Blaise Pascal, Complexe Scientifique des Cézeaux, Aubière Cedex 63177, France
Received 21 December 2002

Abstract

Goldman points of a topological space are defined in order to extend the notion of prime G-ideals of a ring. We associate to any topological space a new topology called Goldman topology. For sober spaces, we prove an extension theorem of continuous maps. As an application, we give a topological characterization of the Jacobson subspace of the spectrum of a commutative ring. Many examples are provided to illustrate the theory.