  We generalize the notions of $\beta$- and $\lambda$-maps to general
selections of sublocales, obtaining different classes of localic maps. These
new classes of maps are used to characterize almost normality, extremal
disconnectedness, $F$-frames, $Oz$-frames, among others types of locales, in a
manner akin to the characterization of normal locales via $\beta$-maps. As a
byproduct we obtain a characterization of localic maps that preserve the
completely below relation (that is, the right adjoints of assertive frame
homomorphisms).
