F-nodec spaces

• Dridi, Lobna ^[2] ; Mhemdi, Abdelwaheb ^[1] ; Turki, Tarek ^[3]
  1. [1] Higher Institute of applied sciences and technologies of Gafsa
  2. [2] University of Tunis
  3. [3] University Tunis-El Manar

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 16, Nº. 1, 2015, págs. 53-64
• Idioma: inglés
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• Resumen

  • Following Van Douwen, a topological space is said to be nodec if it satises 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, and FH functors are completely studied.Secondly, we characterize maps f given by a ow (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.