Infinite group with cofinite topology is a quasitopological group
Then, with this topology, is a quasitopological group: the left multiplication map, right multiplication map, and inverse map are all continuous maps from to itself.
For a set with the cofinite topology, every bijection from the set to itself is a self-homeomorphism. In particular, this means that each of these is a self-homeomorphism:
- The left multiplication map by any fixed element.
- The right multiplication map by any fixed element.
- The inverse map.
Thus, the group is a quasitopological group.