We generalize the notions of β- and λ-maps in terms of selections of sublocales, obtaining different classes of localic maps. These new classes of maps are used to characterize almost normal, extremally disconnected, F- and Oz-locales, among other types of locales, in a manner akin to the characterization of normal locales via β-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).