On hyperconnected spaces (Q1114958)

A topological space is hyperconnected if intersection of any two non- empty open sets is non-empty. This paper gives a characterization of hyperconnected spaces, using the concept of semi-open sets, which yields an alternate proof of Noiri's result [\textit{T. Noiri}, Rev. Roum. Math. Pures Appl. 25, 1091-1094 (1980; Zbl 0459.54012)] that hyperconnectedness is a semi-topological property. Further it is proved that a hyperconnected door space is maximal hyperconnected and minimal door and analyze certain related concepts too.