## On ideal topological spaces via cozero sets.(English)Zbl 1365.54002

Summary: In this paper, we introduce and investigate $$z$$-local function and its properties in ideal topological space. A subset $$H$$ of a space $$X$$ is a zero set if there is a continuous real-valued $$f: X\to\mathbb{R}$$ with $$H= f^{-1}(0)$$, and $$U\subseteq X$$ is a cozero set if $$X-U$$ is a zero set.
We construct a topology $$\tau^*_z$$ for $$X$$ by using the cozero sets and an ideal $${\mathcal I}$$ on $$X$$. Moreover, we obtain characterizations of $$z$$-compatibility of $$\tau$$ with $${\mathcal I}$$ via cozero sets.

### MSC:

 54A05 Topological spaces and generalizations (closure spaces, etc.) 54C10 Special maps on topological spaces (open, closed, perfect, etc.)