F-door spaces and F-submaximal spaces


  • Lobna Dridi University of Tunis
  • Sami Lazaar University Tunis-El Manar
  • Tarek Turki University Tunis-El Manar




Categories, Functors, Door spaces, Submaximal spaces, Primal spaces


Submaximal spaces and door spaces play an enigmatic role in topology. In this paper, reinforcing this role, we are concerned with reaching two main goals:

The first one is to characterize topological spaces X such that F(X) is a submaximal space (resp., door space) for some covariant functor Ff rom the category Top to itself. T0, and FH functors are completely studied.

Secondly, our interest is directed towards the characterization of maps f given by a flow (X, f) in the category Set, such that (X,P(f)) is submaximal (resp., door) where P(f) is a topology on X whose closed sets are exactly the f-invariant sets.


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Author Biographies

Lobna Dridi, University of Tunis

Department of Mathematics, Tunis Preparatory Engineering Institute. University of Tunis. 1089 Tunis, Tunisia.

Sami Lazaar, University Tunis-El Manar

Department of Mathematics, Faculty of Sciences of Tunis. University Tunis-El Manar. “Campus Universitaire” 2092 Tunis, Tunisia.

Tarek Turki, University Tunis-El Manar

Department of Mathematics, Faculty of Sciences of Tunis. University Tunis-El Manar. “Campus Universitaire” 2092 Tunis, Tunisia.


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How to Cite

L. Dridi, S. Lazaar, and T. Turki, “F-door spaces and F-submaximal spaces”, Appl. Gen. Topol., vol. 14, no. 1, pp. 97–113, Apr. 2013.



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