Paratopological group not implies topological group
From Groupprops
Statement
There are two versions:
- Weak version: It is possible to construct a paratopological group that is not a topological group.
- Strong version: It is possible to construct a topological space that occurs as the underlying space of a paratopological group but does not occur as the underlying space of any topological group.
Proof
Example of the Sorgenfrey line
Further information: Sorgenfrey line