F-nodec spaces

Lobna Dridi; Abdelwaheb Mhemdi; Tarek Turki

doi:10.4995/agt.2015.3141

Authors

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

DOI:

https://doi.org/10.4995/agt.2015.3141

Keywords:

Categories, functors, Nodec spaces, primal Space.

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.

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Author Biography

Lobna Dridi, University of Tunis

PREPARATORY ENGINEERING INSTITUTE. DEPARTEMENT OF MATHEMATICS

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