On some maps concerning g??-open sets


  • Miguel Caldas Cueva Universidade Federal Fluminense.
  • Saeid Jafari College of Vestsjaelland South.




Topological spaces, βθ-closed sets, βθ-open sets, βθ-open maps, β-irresolute maps, βθ-T1 spaces.


In this paper, we consider a new notion of ??-open maps via the concept of g??-closed sets which we call approximately ??-open maps. We study some of its fundamental properties. It turns out that we can use this notion to obtain a new characterization of ??-Ti spaces.

Author Biography

Miguel Caldas Cueva, Universidade Federal Fluminense.

Departamento de Matematica Aplicada.


[1] M. E. Abd. El-Monsef, S. N. EL-Deeb and R. A. Mahmoud: ?-open and ?-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12, pp. 77-90, (1983).

[2] D. Andrijevic: Semi-preopen sets, Mat. Vesnik 38, pp. 24-32, (1986).

[3] M. Caldas: Other characterizations of ?-?-R0 topological spaces, Tamkang Jour. of Math., 44, pp. 303-311, (2013).

[4] M. Caldas: On ?-?-generalized closed sets snd ?-?-generalized continuity in topolological spaces, J. Adv. Math. Studies, 4, pp. 13-24, (2011).

[5] M. Caldas, Weakly sp-?-closed functions and semipre-Hausdorff spaces, Creative Math. Inform., 20, 2, pp. 112-123, (2011).

[6] M. Caldas, Functions with strongly ?-?-closed graphs, J. Adv. Studies Topology, 3, pp. 1-6, (2012).

[7] M. Caldas, On characterizations of weak ?-?-openness, Antartica J. Math., 9(3) , pp. 195-203, (2012).

[8] M. Caldas, On contra ??-continuous functions, Proyecciones Journal Math. 39, 4, pp. 333-342, (2013).

[9] S. Jafari and T. Noiri: On ?-quasi irresolute functions, Mem. Fac. Sci. Kochi Uni.(math), 21, pp. 53-62, (2000).

[10] T. Noiri, Weak and strong forms of ?-irresolute functions, Acta Math. Hungar., 99, pp. 315-328, (2003).

[11] D.A.. Rose: On weak openess and almost openness, Internat. J. Math. and Math. Sci., 7, pp. 35-40, (1984).

How to Cite

M. Caldas Cueva and S. Jafari, “On some maps concerning g??-open sets”, Proyecciones (Antofagasta, On line), vol. 34, no. 1, pp. 15-24, 1.