On separation axioms in ideal topological spaces

Abstract

Separation axioms in ideal topological spaces are discussed in the literature. In this paper we define the separation axioms in ideal topological spaces in a new way which is more natural than the previous versions and discuss some properties. Also we discuss the relationship of our definition with other definitions and prove some results in the context of separation axioms in ideal topological space. We show a property that holds in ideal topological theory which does not hold in the classical theory of topology; and also we show aproperty that holds in the classical theory that does not hold in the ideal topological theory.