On Z-open sets

Abstract

Continuous real valued function is an important tool in topology. In
this paper, real valued continuous functions are used to define some kind of
sets called zero sets which is the inverse image of zero of a real valued
function from a topological space, the complement of zero sets is called a
cozero sets, and the family of all cozero sets of a topological space X forms
a base for a topology on X which is called the Z-topology on X and its
elements is called Z-open sets.
In this work we study the properties of these sets with some relations
between it and other sets like open, cozero and zero sets. On the other hand
we proved some results and characterizations with some examples.