The empty set cannot belong to any collection with the finite intersection property. The condition is trivially satisfied if the intersection over the entire collection is non-empty (in particular, if the collection itself is empty), and it is also trivially satisfied if the collection is nested, meaning that the collection is totally ordered by inclusion (equivalently, for any finite subcollection, a particular element of the subcollection is contained in all the other elements of the subcollection), e.g. the nested sequence of intervals (0, 1/"n"). However, these are not the only possibilities. For example, if "X" = (0, 1) and for each positive integer "i", "Xi" is the set of elements of "X" having a decimal expansion with digit 0 in the "i"th decimal place, then any finite intersection is non-empty (just take 0 in those finitely many places and 1 in the rest), but the intersection of all "Xi" for "i" ≥ 1 is empty, since no element of (0, 1) has all zero digits.