Mathematically precise definitions of various topological properties were given. To investigate Piaget's theory that topological relationships are mastered before certain Euclidean ones, 58 subjects of 3 to 7 years old were asked to divide 14 items depicting topological and Euclidean properties into groups of "things they felt were alike." Younger children used significantly stronger topological classification techniques while older ones used significantly stronger Euclidean classification techniques. The suggestion was made that the topological intuition of 3-year-olds may be superseded by strongly reinforced Euclidean notions.