A subframe is a subobject in the category Frm of frames. More explicitly, if is a frame, then a subframe of is a subset of the underlying set of such that is closed under arbitrary joins and finitary meets (including having the bottom and top elements).
In the correspondence between frames and locales, a subframe corresponds to a kind of quotient locale. However, only regular quotients of locales behave as quotient spaces for the purposes of topology. These correspond to regular subframes; not all subframes are regular.
Is there a convenient elementary description of when a subframe is regular?