F-nodec spaces

[EN] Following Van Douwen, a topological space is said to be nodec if it satisfies one of the following equivalent conditions: (i) every nowhere dense subset of X, is closed; (ii) every nowhere dense subset of X, is closed discrete; (iii) every subset containing a dense open subset is open. This pap...

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Detalles Bibliográficos
Autores: Dridi, Lobna, Mhemdi, Abdelwaheb, Turki, Tarek
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/50175
Acceso en línea:https://riunet.upv.es/handle/10251/50175
Access Level:acceso abierto
Palabra clave:Categories
Functors
Nodec spaces
Primal Space
Descripción
Sumario:[EN] Following Van Douwen, a topological space is said to be nodec if it satisfies one of the following equivalent conditions: (i) every nowhere dense subset of X, is closed; (ii) every nowhere dense subset of X, is closed discrete; (iii) every subset containing a dense open subset is open. This paper deals with a characterization of topological spaces X such that F(X) is a nodec space for some covariant functor F from the category Top to itself. T0 , ρ and FH functors are completely studied. Secondly, we characterize maps f given by a flow (X, f ) in the category Set such that (X, P(f )) is nodec (resp., T0-nodec), where P(f ) is a topology on X whose closed sets are precisely f-invariant sets.