In general topology, a branch of mathematics, the Appert topology, named for Antoine Appert (1934), is a topology on the set X = {1, 2, 3, ...} of positive integers.[1] In the Appert topology, the open sets are those that do not contain 1, and those that asymptotically contain almost every positive integer. The space X with the Appert topology is called the Appert space.[1]