In mathematics, and especially in order theory, a nucleus is a function on a meet-semilattice such that (for every in ):
Every nucleus is evidently a monotone function.
Frames and locales
Usually, the term nucleus is used in frames and locales theory (when the semilattice is a frame).
Proposition: If is a nucleus on a frame , then the poset of fixed points of , with order inherited from , is also a frame.