Minimal open sets on generalized topological space.

Authors

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

Keywords:

Generalized topology, Minimal μ-open sets, μ-pre-Hausdorff space

Abstract

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.

Author Biographies

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.

References

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

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

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

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

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

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

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

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).

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

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

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).

How to Cite

[1]
C. Carpintero, E. Rosas, M. Salas-Brown, and J. Sanabria, “Minimal open sets on generalized topological space.”, Proyecciones (Antofagasta, On line), vol. 36, no. 4, pp. 739-751, 1.

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Artículos