Suppose is a group (viewed purely as an abstract group). The Marjov topology of is defined as the topology where the closed subsets are precisely the unconditionally closed subsets of (this means that the subset is closed for any topology on ).
Note that although all subsets in the Markov topology are closed subsets for any T0 topological group structure of , it is not necessary that under the Markov topology would itself be a topological group. In fact, it is often not a topological group. However, it is a quasitopological group (see Markov topology defines a quasitopological group).
For instance, the Markov topology on the group of integers is the cofinite topology, which makes it a quasitopological group (see infinite group with cofinite topology is a quasitopological group) but not a topological group (see infinite group with cofinite topology is not a topological group).