## An extension theorem for sober spaces and the Goldman topology.(English)Zbl 1042.54003

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.

### MSC:

 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 54B35 Spectra in general topology 54F65 Topological characterizations of particular spaces 57R30 Foliations in differential topology; geometric theory
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