Abstract
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. T-0, p 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., To-nodec), where P(f) is a topology on X whose closed sets are precisely f -invariant sets.