Quasitopological group not implies topological group

Statement
It is possible to have a quasitopological group that is not a topological group.

Related facts

 * Topological group implies quasitopological group
 * Algebraic group implies quasitopological group
 * Algebraic group not implies topological group

Facts used

 * 1) uses::Infinite group with cofinite topology is a quasitopological group
 * 2) uses::Infinite group with cofinite topology is not a topological group

Proof
The proof follows directly form Facts (1) and (2) and the observation that infinite groups exist.