F-nodec spaces

Abstract

[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.