Paratopological group not implies topological group

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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

References