The Fort space is a refinement of the Appert topology.

A subset of Z is compact in the Appert topology if and only if it is finite.

In the Appert topology, the open sets are those that do not contain 1, and those that asymptotically contain almost every positive integer.

The Appert topology is closely related to the Fort space topology that arises from giving the set of integers greater than one the discrete topology, and then taking the point 1 as the point at infinity in a one point compactification of the space.