New separation axioms in generalized topological spaces (Q653940)

A family \(\mu\) of subsets of a set \(X\) is called a general topology on \(X\) if \(\mu\) is closed under arbitrary unions and \(\emptyset\in\mu\). All these \((X,\mu)\)'s are called generalized topological spaces (briefly, GTS), as generalizations of topological spaces. The T\(_0\)- and T\(_1\)-separation axioms can be similarly defined in generalized topological spaces as in topological spaces, called \(\mu\)-T\(_0\) and \(\mu\)-T\(_1\), respectively. In this paper, the author introduces some new separation axioms lying between \(\mu\)-T\(_0\) and \(\mu\)-T\(_1\) in generalized topological spaces, namely, \(\mu\)-T\(_{\frac{1}{2}}\), \(\mu\)-T\(_{\frac{1}{4}}\) and \(\mu\)-T\(_{\frac{3}{8}}\). Some characterizations of these separation axioms are given. Also the author discusses the relations between these new separation axioms and some of other ones in GTSs.