An example of a countable double-pointed cofinite topology is the set of even and odd integers, with a topology that groups them together. Let "X" be the set of integers, and let "O""A" be a subset of the integers whose complement is the set "A". Define a subbase of open sets "G""x" for any integer "x" to be "G""x" = "O"{"x", "x"+1} if "x" is an even number, and "G""x" = "O"{"x"-1, "x"} if "x" is odd. Then the basis sets of "X" are generated by finite intersections, that is, for finite "A", the open sets of the topology are