A regular element of a Heyting algebra is an element such that .
Thus a Boolean algebra is precisely a Heyting algebra in which every element is regular.
Analogously, a regular open set in a topological space is a regular element of the frame of open sets of ; equivalently, an open set which equals the interior of its closure, or equivalently the exterior of its exterior. (This is the origin of the term, related to a regular space.)
The regularisation of is ; note that this is regular. In fact, any element of the form is regular.