An extension theorem for sober spaces and the goldman topology

Ezzeddine Bouacida; Othman Echi; Gabriel Picavet; Ezzeddine Salhi

doi:10.1155/S0161171203212230

An extension theorem for sober spaces and the goldman topology

Ezzeddine Bouacida
, Othman Echi
, Gabriel Picavet
, Ezzeddine Salhi

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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.

Original language	English
Pages (from-to)	3217-3239
Number of pages	23
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	2003
Issue number	51
DOIs	https://doi.org/10.1155/S0161171203212230
State	Published - 2003
Externally published	Yes

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1155/S0161171203212230

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title = "An extension theorem for sober spaces and the goldman topology",

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.",

author = "Ezzeddine Bouacida and Othman Echi and Gabriel Picavet and Ezzeddine Salhi",

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AU - Bouacida, Ezzeddine

AU - Echi, Othman

AU - Picavet, Gabriel

AU - Salhi, Ezzeddine

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/13444294317

U2 - 10.1155/S0161171203212230

DO - 10.1155/S0161171203212230

M3 - Article

AN - SCOPUS:13444294317

SN - 0161-1712

VL - 2003

SP - 3217

EP - 3239

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

IS - 51

ER -

An extension theorem for sober spaces and the goldman topology

Abstract

ASJC Scopus subject areas

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