Topological Group - Generalizations

Generalizations

Various generalizations of topological groups can be obtained by weakening the continuity conditions:

• A semitopological group is a group G with a topology such that for each c in G the two functions G → G defined by and are continuous.
• A quasitopological group is a semitopological group in which the function mapping elements to their inverses is also continuous.
• A paratopological group is a group with a topology such that the group operation is continuous.