Separation Axioms in Generalized Base Spaces

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.