×

zbMATH — the first resource for mathematics

On \(\theta\)-\(C\)-open sets. (English) Zbl 0774.54018
For a space \(X\) and \(A\subseteq X\), recall that \(\text{cl}_ \theta A=\{x\in X\): every closed neighborhood of \(x\) meets \(A\}\). A function \(f:X\to Y\), where \(X\) and \(Y\) are spaces, is \(\theta\)-\(C\)-continuous if for every closed \(A\subset Y\), \(f^ \leftarrow[A]=\text{cl}_ \theta B\) for some \(B\subseteq X\). Properties of \(\theta\)-\(C\)-continuous functions are developed, and applications to \(H\)-closed spaces are presented.
MSC:
54D25 “\(P\)-minimal” and “\(P\)-closed” spaces
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
PDF BibTeX XML Cite
Full Text: DOI EuDML