Bicompleting the left quasi-uniformity of a paratopological group
Extending results from the theory of topological groups to paratopological groups, the authors show that the bicompletion of the left quasi-uniformity of a paratopological \((T_0)\)-group \(G\) can be considered a topological semigroup which contains \(G\) as a sup-dense subsemigroup. Furthermore they characterize those paratopological \((T_0)\)-groups \(G\) for which the bicompletion of the left quasi-uniformity is a group \(H\) by the condition that each filter which is Cauchy with respect to the left uniformity is also Cauchy with respect to the right uniformity of the topological group associated with \(G\); under the latter condition the bicompleted left quasi-uniformity of \(G\) yields the left quasi-uniformity of the paratopological group \(H\). \{A paratopological group is a pair \((G,\tau)\) where \(G\) is a group and \(\tau\) is a topology on \(G\) such that the function \(\Psi: (G\times G,\tau\times \tau)\to (G,\tau)\) defined by \(\Psi(x,y)= xy\) is continuous\}.
scientific article; zbMATH DE number 1145389