subframe

A **subframe** is a subobject in the category Frm of frames. More explicitly, if $L$ is a frame, then a **subframe** of $L$ is a subset $M$ of the underlying set of $L$ such that $M$ 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?