 The open interval (0, 1) has an Euler characteristic of −1, so its power set 2(0, 1) should have an Euler characteristic of 2−1 = 1/2.The appropriate power set to take is the "small power set" of finite subsets of the interval, which consists of the union of a point (the empty set), an open interval (the set of singletons), an open triangle, and so on.So the Euler characteristic of the small power set is .