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.

Full Text:

PDF

References

K. Belaid and L. Dridi, I-spaces, nodec spaces and compactifications, Topology Appl. 161 (2014), 196-205. (http://dx.doi.org/10.1016/j.topol.2013.10.021)

K. Belaid, O. Echi and S. Lazaar, $T_{(alpha , beta )$-spaces and the Wallman compactification, Int. J. Math. Math. Sc. 68 (2004), 3717-3735. (http://dx.doi.org/10.1155/S0161171204404050)

O. Echi and S. Lazaar, Reflective subcategories, Tychonoff spaces, and spectral spaces, Top. Proc. 34 (2009), 307-319.

A. Grothendieck and J. Dieudonné, Eléments de géométrie algébrique I: le langage des schemas, Inst. Hautes Etudes Sci. Publ. Math. no. 4, 1960.

J. F. Kennisson, The cyclic spectrum of a boolean flow, Theory Appl. Categ. 10 (2002), 392-409.

J. F. Kennisson, Spectra of finitely generated boolean flows, Theory Appl. Categ. 16 (2006), 434-459.

J. W. Tukey, Convergence and uniformity in topology, Annals of Mathematics Studies, no. 2. Princeton University Press, (1940) Princeton, N. J.

R. C. Walker, The Stone-Cech compactification, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 83. New York-Berlin: Springer-Verlag, (1974).

E. Hewitt, A problem of a set theoretic topology, Duke Mat. J. 10 (1943), 309-333. (http://dx.doi.org/10.1215/S0012-7094-43-01029-4)

A. V. Arhangel'skii and P. J. Collins, On submaximal spaces, Topology Appl. 64 (1995), 219-241. (http://dx.doi.org/10.1016/0166-8641(94)00093-I)

E. K. van Douwen, Applications of maximal topologies, Topology Appl. 51 (1993), 125-240. (http://dx.doi.org/10.1016/0166-8641(93)90145-4)

O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970. (http://dx.doi.org/10.2140/pjm.1965.15.961)

G. Bezhanishvili, L. Esakia and D. Gabelaia, Modal Logics of submaximal and nodec spaces, collection of Essays Dedicated to Dick De Jongh on occasion of his 65th. Birthday, J. van Benthem, F. Veltman, A. Troelstra, A. Visser, editors. (2004), pp. 1-13.

L. Dridi, S. Lazaar and T. Turki, F-Door Spaces and F-Submaximal Spaces, Appl. Gen. Topol. 14, no. 1 (2013), 97-113. (http://dx.doi.org/10.4995/agt.2013.1621)

S. Lazaar, On functionally Hausdorff Spaces, Missouri J. Math. Sci. 1 (2013), 88-97.

Abstract Views

4303
Metrics Loading ...

Metrics powered by PLOS ALM


 

Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. F-n-resolvable spaces and compactifications
Intissar Dahane, Lobna Dridi, Sami Lazaar
Applied General Topology  vol: 20  issue: 1  first page: 97  year: 2019  
doi: 10.4995/agt.2019.10036



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt