Ahmad, B.; Noiri, T. The inverse images of hyperconnected sets. (English) Zbl 0607.54016 Mat. Vesn. 37, 177-181 (1985). The authors prove two results: (1) the \(\alpha\)-continuous image of a semi-open hyperconnected set is hyperconnected, (2) preopen hyperconnected sets are inverse preserved under semi-closed preserving surjections with preopen hyperconnected point inverses. Recall that a topological space X is said to be hyperconnected if each non-empty open set in X is dense in X, and that a subset of X is said to be a hyperconnected set if it is hyperconnected as a subspace. Reviewer: I.L.Reilly Cited in 2 Documents MSC: 54D05 Connected and locally connected spaces (general aspects) Keywords:\(\alpha \)-continuous image; semi-open hyperconnected set; preopen hyperconnected sets; semi-closed preserving surjections; preopen hyperconnected point inverses PDFBibTeX XMLCite \textit{B. Ahmad} and \textit{T. Noiri}, Mat. Vesn. 37, 177--181 (1985; Zbl 0607.54016)