SEPARATION PROPERTIES IN IDEAL CLOSURE SPACES

Separation axioms constitute a classical topic in general topology. These axioms are statements about richness of topology. These axioms concern, the separation of points, point from closed sets and closed set from each other. Separation axioms in closure spaces have implication than corresponding axioms in topological spaces. According to E. Cech[2], a closure space is said to be separated if any two distinct points are separated by distinct neighbourhood. W.J. Thron[5] studied higher separation properties in closure spaces. The present paper aims at studying the higher separation axioms of ideal closure spaces. The main purpose of this paper to study the properties of regular spaces, normal spaces and completely normal spaces. we also have discuss a series of theorems and important results as well as basic concepts and the relationships of it.