CUBO A Mathematical Journal Vol.12, N°02, (123–126). June 2010

A note on generalized topological spaces and preorder

Saeid Jafari, Raja Mohammad Latif and Seithuti P. Moshokoa

College of Vestsjaelland South, Herrestraede 11, 4200 Slagelse, Denmark, email: jafari@stofanet.dk

Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. email: raja@kfupm.edu.sa

Department of Mathematical Sciences, University of South Africa, P.O. Box 392, Pretoria 0003, South Africa. email: moshosp@unisa.ac.za

ABSTRACT

This paper deals with the notion of continuity in ordered generalized topological spaces. We also characterize general topological spaces satisfying the Hausdorff property via the graph of the preorder assigned to the general topological space.

Key words and phrases: Topological Spaces, Hausdorff, preorder.

RESUMEN

Este artículo trata de continuidad en espacios topológicos ordenados. También caracterizamos espacios topológicos generalizados satisfaciendo la propiedad de Hausdorff vía el grafo designado de un espacio topológico general preordenado.

AMS Subject Classification (2000): 54D10

References

[1] A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351- 357.        [ Links ]

[2] A. Csaszar, δ- and θ- modifications of generalized topologies, Acta. Math. Hungar., to appear.         [ Links ]

Received: January 2009.

Revised: March 2009.