(i, j)-ω-semiopen sets and (i, j)-ω-semicontinuity in bitopological spaces

Carlos Carpintero¹ & Ennis Rosas¹ & Sabir Hussain²

¹ Department of Mathematics, Universidad De Oriente, Nucleo De Sucre Cumana, Venezuela. Facultad de Ciencias Basicas, Universidad del Atlantico, Barranquilla, Colombia. carpintero.carlos@gmail.com, ennisrafael@gmail.com

² Department of Mathematics, College of Science, Qassim University, P.O.BOX 6644, Buraydah 51482, Saudi Arabia. sabiriub@yahoo.com, sh.hussain@qu.edu.sa

ABSTRACT

The aim of this paper is to introduce and characterize the notions of (i, j)-ω-semiopen sets as a generalization of (i, j)-semiopen sets in bitopological spaces. We also define and discuss the properties of (i, j)-ω-semicontinuous functions.

Keywords and Phrases: Bitopological spaces, (i, j)-ω-semiopen sets, (i, j)-ω-semiclosed sets.
2010 AMS Mathematics Subject Classification: 54A05,54C05,54C08.

RESUMEN

El objetivo de este artículo es introducir y caracterizar las nociones de conjuntos (i, j)- ω-semiabiertos como una generalización de conjuntos (i, j)-semiabiertos en espacios bitopológicos. También definimos y discutimos las propiedades de funciones (i, j)-ω- semicontinuas.

References

[1] S. Bose, Semi-open sets, Semi-Continuity and semi-open mappings in bitopological spaces, Bull. Calcutta Math. Soc., 73(1981), 237-246.
[2] H. Z. Hdeib, ω-closed mappings, Revista Colombiana Mat., 16(1982), 65-78.
[3] J. C. Kelly, Bitopological spaces, Proc. London Math. Soc., 13, pp. 71-89, (1963).
[4] H. Maki, R. Chandrasekhara Rao and A. Nagoor Gani, On generalizing semi-open sets and preopen sets, Pure Appl. Math. Math. Sci, 49 (1999), pp 17-29.
[5] W. J. Pervin, Connectedness in Bitopological spaces, Ind. Math., 29 (1967), 369-372.

Received: March 2015. Accepted: May 2015.