Noiri, T.; Popa, V. On almost \(\beta\)-continuous functions. (English) Zbl 0901.54011 Acta Math. Hung. 79, No. 4, 329-339 (1998). A subset \(A\) of a topological space \(X\) is called \(\beta\)-open if \(A\subset \text{Cl}(\text{Int}(\text{Cl}(A)))\). A function \(f:X\to Y\) is called almost \(\beta\)-continuous at \(x\in X\) if for every open neighbourhood \(V\) of \(f(x)\) there exists a \(\beta\)-open set \(U\) containing \(x\) such that \(f(U)\subset \text{Int} (\text{Cl}(V))\). Several characterizations, sufficient conditions, and necessary conditions of almost \(\beta\)-continuity are encountered. Reviewer: Zoltán Boros (Debrecen) Cited in 1 ReviewCited in 3 Documents MSC: 54C08 Weak and generalized continuity 54C10 Special maps on topological spaces (open, closed, perfect, etc.) Keywords:regular space; continuous function; semi-preopen set PDFBibTeX XMLCite \textit{T. Noiri} and \textit{V. Popa}, Acta Math. Hung. 79, No. 4, 329--339 (1998; Zbl 0901.54011) Full Text: DOI