Cofinite Topology

Some articles on cofinite topology, topology:

Cofiniteness - Cofinite Topology - Double-pointed Cofinite Topology
... The double-pointed cofinite topology is the cofinite topology with every point doubled that is, it is the topological product of the cofinite topology with the indiscrete ... An example of a countable double-pointed cofinite topology is the set of even and odd integers, with a topology that groups them together ... is, for finite A, the open sets of the topology are The resulting space is not T0 (and hence not T1), because the points x and x + 1 (for x even) are topologically indistinguishable ...
T1 Space - Examples
... Sierpinski space is a simple example of a topology that is T0 but is not T1 ... The overlapping interval topology is a simple example of a topology that is T0 but is not T1 ... The cofinite topology on an infinite set is a simple example of a topology that is T1 but is not Hausdorff (T2) ...