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Quasi-homeomorphisms, Goldspectral spaces and Jacspectral spaces

Othman Echi — 2003

Bollettino dell'Unione Matematica Italiana

In this paper, we deal with the study of quasi-homeomorphisms, the Goldman prime spectrum and the Jacobson prime spectrum of a commutative ring. We prove that, if g : Y X is a quasi-homeomorphism, Z a sober space and f : Y Z a continuous map, then there exists a unique continuous map F : X Z such that F g = f . Let X be a T 0 -space, q : X s X the injection of X onto its sobrification X s . It is shown, here, that q Gold X = Gold X s , where Gold X is the set of all locally closed points of X . Some applications are also indicated. The Jacobson prime spectrum...

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