Separation Axioms in Generalized Base Spaces
Kamal El-Saady
Department of Mathematics, Faculty of Science at Qena, South Valley University, Qena 83523, Egypt.
Fatima Al-Nabbat *
Department of Mathematics, College of Science, King Faisal University, Al-Hasa, 31982, P.O.Box 380, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
The concept of generalized base space is given as a generalization of closure spaces, kernel spaces, topological spaces. The purpose of this paper is to study and investigate some separations axioms in the so-called generalized base spaces. Some characterizations of GBTi-spaces for i = 0, 1, 2, 3, 4 are obtained and some relations among these spaces are established. We study some results concerning separation axioms which are true in general topology, but it is not true in the generalized base spaces.
Keywords: Generalized topologies, weak structures, separation axioms.