The cofinite topology on a set 
consists of the empty set together with every subset whose
complement in 
is finite. On an infinite set it is 
and compact but not Hausdorff. On a finite set it is the
discrete topology.
Cofinite Topology
See also
Compact Space, Discrete Topology, T2-Space, Topological SpaceExplore with Wolfram|Alpha
References
Munkres, J. R. Topology, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 2000.Cite this as:
Weisstein, Eric W. "Cofinite Topology." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CofiniteTopology.html