On the \(\gamma\)-interior and \(\gamma\)-closure of a set (Q1280289)

Let \(X\) be a set and \(\gamma\), some monotone selfmap of \(\exp(X)\). Also, let \(i_{\gamma}\)(=the \(\gamma\)-interior) and \(c_{\gamma}\)(=the \(\gamma\)-closure) be the couple of monotone selfmaps of \(\exp(X)\) introduced as in [\textit{Á. Császár}, Acta Math. Hung. 75, No. 1-2, 65-87 (1997; Zbl 0924.54003)]. The aim of this note is to show that, under suitable conditions upon \(\gamma\), these associated maps can be obtained via explicit formulae.