F-nodec spaces

Lobna Dridi, Abdelwaheb Mhemdi, Tarek Turki

Abstract

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.


Keywords

Categories; functors; Nodec spaces; primal Space.

Subject classification

54B30; 54D10; 54G12; 46M15.

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References

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