Open Lattice Theorem

The Open Lattice Theorem states that in certain mathematical structures called lattices, if you look at all the elements above a particular point (called an "interval"), this subset itself forms a lattice. Moreover, this "interval" lattice is "open," meaning it includes all elements that are greater than or equal to a specific element without missing any in between. Essentially, it says that focusing on a part of the lattice preserves the overall structure, allowing for consistent analysis and operations within that subset as if it were its own complete lattice.