Paratopological group

Definition
A paratopological group is a set $$G$$ endowed with the following two structures:


 * The structure of a group, viz., an associative binary operation with identity element and inverses
 * The structure of a topological space

such that the following are true:

Incomparable structures

 * Quasitopological group means the group multiplication is separately continuous but the inverse map is required to be continuous.