A new decomposition of open and closed sets in topological spaces


  • Carlos Granados Universidad del Atlántico, Barranquilla-Colombia.




*b-open sets, generalized of *b-closed sets, locally *b-closed sets, regular generalized *b-closed sets, weakly *b-closed sets


In this paper, we show some properties on *b-open sets. Besides, we introduce the notions of generalized *b-closed sets, locally *b-closed sets, regular generalized *b-closed sets and weakly *b-closed sets. Moreover, we study some of their properties.


Al-Omari A, Salmi M. Decomposition of continuity via b-open set. Bol. Soc. Paran. Mat. 1996; 26(1-2): 53-64.

Andrijivic D. On b-open sets. Mat. Vesnik. 1996; 48: 59-64.

Gnanambal Y. On generalized pre-regular closed sets in topological spaces. Indian J. Pure Appl. Math. 1997; 28: 351-360.

Granados C. A decomposition of continuity and contra continuity in ideal nano topological spaces. Journal of the international

Mathematical Virtual Institute. 2020; 10(2): 271-286.

Granados C. A decomposition of open sets through operator interior, International Journal of Advances in Applied Mathematics and Mechanics. 2020; 8(2): 15-26.

Granados C. A new notion of convergence on ideal topological spaces, Selecciones Matem´aticas. 2020; 7(2): 250-256.

Hariwan Z. Bc-open sets in topological spaces. Advances in pure Mathematics. 2013; 3: 34-40.

Hdeib H. w-closed mappings. Revista Colombiana de Mat. 1982; 16: 65-78.

Indira T, Rekha K. On locally **b-closed sets. Proceedings of the Heber International Conference on Applications of Mathematics an Statistics. 2012.

Kuratowski K. Topologie I. Monografie Matematyczne tom 3. PWN-Polish Scientific Publishers. Warszawa. 1933.

Levine N. Semi-open sets and semi-continuity in topological spaces. Armer Math. Monthly. 1963; 70: 36-41.

Mariappa K, Sekar S. On regular generalized b-closed set. Int. Journal of Math. Analysis. 2013; 3(13): 613-624.

Mashhour A, El-monsef M, El-deeb S. On pre-continuous and weak pre-continuous mappings. Proc. Math. Phys. Soc. Egypt. 1982; 53:47-53.

Noiri T, Keskin A. On Al -sets and some weak separation axioms. Int. J. Math. Anal. 2011; 5(11): 539-548.

Stone M. Applications of the theory of Boolean rings to general topology. Trans. Armer. Math. Soc. 1937; 41:375-381.

Usha R, Thangavelu P. On locally numeralb-closed sets and weakly numeralb-closed sets. South Asian Journal Of Multidisciplinary

Studies. 2015; 2(3):181-196.




How to Cite

Granados, C. (2021). A new decomposition of open and closed sets in topological spaces. Selecciones Matemáticas, 8(01), 66 - 74. https://doi.org/10.17268/sel.mat.2021.01.06