framesubset
In frame theory, a framesubset (often simply called a subframe) of a frame L is a subset S of L that is itself a frame with the induced order and operations. Concretely, S must contain the bottom and top elements (0 and 1) of L, and be closed under finite meets (finite intersections) and arbitrary joins (unions). Under these conditions, S, with the inherited order, join, and meet, is a frame in its own right.
A framesubset S is equivalent to a frame embedding i: S → L, where the inclusion map preserves
Examples help illustrate the concept. In the power set frame P(X) with union as join and intersection
Framesubsets are relevant in the study of locale theory and point-free topology, where frames model spaces