Minimal open sets on generalized topological space

  • Carlos Carpintero Universidad de Oriente.
  • Ennis Rosas Universidad de la Costa.
  • Margot Salas-Brown Universidad de Oriente.
  • José Sanabria Universidad de Oriente.

Resumen

We introduce the notion of minimal open sets in a generalized topological space (X, μ). We investigate some of their fundamental properties and proved that any subset of a minimal open set on a GTS (X, μ) is a μ-preopen set.

Biografía del autor

Carlos Carpintero, Universidad de Oriente.
Departamento de Matemáticas.
Ennis Rosas, Universidad de la Costa.
Departamento de Ciencias Naturales y Exactas.
Margot Salas-Brown, Universidad de Oriente.
Departamento de Matemáticas.
José Sanabria, Universidad de Oriente.
Departamento de Matemáticas.

Citas

[1] Á. Császár, Generalized topology, generalized continuity. Acta Math. Hungar., 96, pp. 351--357, (2002).

[2] S. Hussain and B. Ahmad, On minimal γ-open sets. EJPAM., 2 (3), pp. 338--351, (2009).

[3] S. Hussain and B. Ahmad, γ-semi-open sets in topological spaces II. Southeast Asian Bull. Math., 34 (5), pp. 997--1008, (2010).

[4] A. B. Khalaf and H. Z. Ibrahim, Some applications of minimal Pγ-open sets. Demonstr. Math., 47 (2), pp. 423-432, (2014).

[5] A. B. Khalaf and S. F. Namiq, On minimal λc-open sets. Asian. J. Fuzzy. Applied Math., 2, pp. 198-202, (2014).

[6] F. Nakaoka and N. Oda, Minimal closed sets and maximal closed sets. Int. J. Math. Math. Sci., pp. 1-8, (2006).

[7] F. Nakaoka and N. Oda, Some applications of minimal open sets. Int. J. Math. Math. Sci., 27 (8), pp. 471-476, (2001).

[8] B. Roy and R. Sen, On maximal μ-open and minimal μ-closed sets via generalized topology. Acta Math. Hungar., 136 (4), pp. 233-239, (2012).

[9] M. Salas B., E. Rosas, C. Carpintero and J. E. Sanabria, On minimal semi open sets on generalized topology. Under preparation.

[10] M. Salas B., E. Rosas, C. Carpintero and J. E. Sanabria, On minimal pre open sets on generalized topology. Under preparation.

[11] A. Vadivel, R. Aishwarya and M. Saraswathi, I -open sets and maximal I -closed sets, J. of Adv. Research in Pure Math., Vol. 3, 1, pp. 87-95, (2011).
Cómo citar
Carpintero, C., Rosas, E., Salas-Brown, M., & Sanabria, J. (1). Minimal open sets on generalized topological space. Proyecciones. Journal of Mathematics, 36(4), 739-751. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2548
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