Editing General topology (section)

====Cofinite and cocountable topologies====
Any set can be given the [[cofinite topology]] in which the open sets are the empty set and the sets whose complement is finite.  This is the smallest [[T1 space|T<sub>1</sub>]] topology on any infinite set.

Any set can be given the [[cocountable topology]], in which a set is defined as open if it is either empty or its complement is countable.  When the set is uncountable, this topology serves as a counterexample in many situations.