Resumen de F-nodec spaces

Lobna Dridi, Abdelwaheb Mhemdi, Tarek Turki

• 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.