Semitopological group

Definition
A semitopological group is a set 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

satisfying the following compatibility conditions:

Facts

 * Algebraic groups are semitopological groups (in fact, they are quasitopological groups) but they are not necessarily topological groups.
 * Locally compact Hausdorff semitopological group implies topological group