Let x = (0, 1] and m = {∅, finite unions of disjoint intervals that are open on the left and closed on the right}. a typical a ∈ m has the form a = sm i=1(ai , bi ], with ai > bi−1. it is easy to see that m is closed under complements and finite unions after noting that the complement of such an interval consists of two disjoint like intervals and the union of two such intervals that overlap is a like interval. the analogous set is not an algebra if x = r - try the complement condition.