F-nodec spaces

• Dridi, Lobna ^[2] ; Mhemdi, Abdelwaheb ^[1] ; Turki, Tarek ^[3]
  1. [1] Higher Institute of applied sciences and technologies of Gafsa
  2. [2] University of Tunis
  3. [3] University Tunis-El Manar

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 16, Nº. 1, 2015, págs. 53-64
• Idioma: inglés
• DOI: 10.4995/agt.2015.3141
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• Resumen

  • 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.

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