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