F-nodec spaces


  • Lobna Dridi University of Tunis
  • Abdelwaheb Mhemdi Higher Institute of applied sciences and technologies of Gafsa
  • Tarek Turki University Tunis-El Manar




Categories, functors, Nodec spaces, primal Space.


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.


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Author Biography

Lobna Dridi, University of Tunis



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How to Cite

L. Dridi, A. Mhemdi, and T. Turki, “F-nodec spaces”, Appl. Gen. Topol., vol. 16, no. 1, pp. 53–64, Mar. 2015.